Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds

From MaRDI portal
Publication:1168597

DOI10.4310/jdg/1214436699zbMath0493.53035OpenAlexW1570658674WikidataQ115188080 ScholiaQ115188080MaRDI QIDQ1168597

Jeff Cheeger, Michael E. Taylor, Mikhael Gromov

Publication date: 1982

Published in: Journal of Differential Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4310/jdg/1214436699



Related Items

Product formula for imaginary resolvents with application to a modified Feynman integral, Heat kernel bounds, conservation of probability and the Feller property, Comparaison des champs de vecteurs et des puissances du Laplacien sur une variété Riemannienne à courbure non positive, Integral curvature bounds and diameter estimates on Finsler manifolds, On the long-time behavior of immortal Ricci flows, Hardy-Littlewood theory for semigroups, On the parabolic kernel of the Schrödinger operator, Yamabe metrics of positive scalar curvature and conformally flat manifolds, Paley-Wiener approximations and multiscale approximations in Sobolev and Besov spaces on manifolds, The atomic decomposition of weighted Hardy spaces associated to self-adjoint operators on product spaces, Stochastic differential equations on noncompact manifolds: Moment stability and its topological consequences, Oscillating multipliers on Lie groups and Riemannian manifolds, Essential spectrum and heat kernel, Infinitesimal transformations on noncompact manifold, Well-posedness and regularity for the elasticity equation with mixed boundary conditions on polyhedral domains and domains with cracks, Minimality of the horocycle flow on laminations by hyperbolic surfaces with non-trivial topology, L p spectral theory of Kleinian groups, Restriction estimates, sharp spectral multipliers and endpoint estimates for Bochner-Riesz means, Some properties of non-compact complete Riemannian manifolds, Minimal surfaces and 3-manifolds of non-negative Ricci curvature, Density and spectrum of minimal submanifolds in space forms, On \(\kappa\)-noncollapsed complete noncompact shrinking gradient Ricci solitons which split at infinity, Nodal sets of eigenfunctions on Riemannian manifolds, Regularity results for pluriclosed flow, Optimal regularization processes on complete Riemannian manifolds, Adiabatic decomposition of the \(\zeta\)-determinant and scattering theory, Some nonlinear function theoretic properties of Riemannian manifolds, Sobolev theorems for cusp manifolds, Pointwise Fourier inversion: A wave equation approach, Injectivity radius bound of Ricci flow with positive Ricci curvature and applications, Hardy spaces associated to Schrödinger operators on product spaces, Structure theory and convergence in Riemannian geometry, Spectral multipliers for Hardy spaces associated to non-negative self-adjoint operators satisfying Davies-Gaffney estimates, Riesz transformations on a class of manifolds with conical singularities, How to produce a Ricci flow via Cheeger-Gromoll exhaustion, On complete noncompact Kähler manifolds with positive bisectional curvature, Remark on a paper of E. Ghys, Spectral asymptotics revisited, A BLW inequality for vector bundles and applications to spectral bounds, Finite propagation speed for solutions of the wave equation on metric graphs, Regularity for the harmonic-Einstein equation, Spectral multipliers for Schrödinger operators, Ricci curvature, radial curvature and large volume growth, Determinant fiber bundles, Quillen metric and degeneracy of curves., Families index for manifolds with boundary, superconnections and cones. II: The Chern character, Parabolic Harnack inequality on metric spaces with a generalized volume property, Triangulating smooth submanifolds with light scaffolding, Kernels of elliptic operators: bounds and summability, Analytic factorization of Lie group representations, Wavelet frames, Sobolev embeddings and negative spectrum of Schrödinger operators on manifolds with bounded geometry, A compactness theorem for complete Ricci shrinkers, Semi-classical functional calculus on manifolds with ends and weighted \(L^p\) estimates, The longitudinal cocycle and the index of Toeplitz operators, Surfaces with boundary: their uniformizations, determinants of Laplacians, and isospectrality, Properties of the probability density function of the non-central chi-squared distribution, Asymptotic finite propagation speed for heat diffusion on certain Riemannian manifolds, Nodal domains and growth of harmonic functions on noncompact manifolds, Sharp estimates for some functions of the Laplacian on noncompact symmetric spaces, Relative index theory, On the solutions to certain Laplace inequalities with applications to geometry of submanifolds, Every conformal class contains a metric of bounded geometry, Asymptotic Dirichlet problem for \(\mathcal {A}\)-harmonic functions on manifolds with pinched curvature, \(\overline\partial\)-torsion for complex manifolds and the adiabatic limit, Weighted Hardy spaces associated to self-adjoint operators and \(bmo_{l,w}\), Marcinkiewicz-type spectral multipliers on Hardy and Lebesgue spaces on product spaces of homogeneous type, Injectivity radius of Lorentzian manifolds, On the chaotic behavior of the Dunkl heat semigroup on weighted \(L^{p}\) spaces, The index of the scattering operator on the positive spectral subspace, Hadamard states for the Klein-Gordon equation on Lorentzian manifolds of bounded geometry, Pointwise bounds for \(L^{2}\) eigenfunctions on locally symmetric spaces, Monotonicity rule for the quotient of two functions and its application, Atomic decomposition of Hardy type spaces on certain noncompact manifolds, On the conditions to control curvature tensors of Ricci flow, On breakdown criteria for nonvacuum Einstein equations, Higher eta-invariants, Areas and volumes for null cones, A local curvature bound in Ricci flow, Non-singular solutions of normalized Ricci flow on noncompact manifolds of finite volume, Extremal of log Sobolev inequality and \(W\) entropy on noncompact manifolds, \(L^ p\)-estimates on functions of the Laplace operator, Riesz transforms associated to Schrödinger operators on weighted Hardy spaces, Notes on Perelman's papers, On Calabi's conjecture for complex surfaces with positive first Chern class, Gradient estimate for the heat kernel of a complete Riemannian manifold and its applications, \(L^ p\) and mean value properties of subharmonic functions on Riemannian manifolds, Local foliations and optimal regularity of Einstein spacetimes, Hardy spaces and bmo on manifolds with bounded geometry, Weighted Sobolev spaces and regularity for polyhedral domains, Heat kernel on manifolds with ends, Continuity properties of the integrated density of states on manifolds, Chern-Ricci flows on noncompact complex manifolds, Riesz potentials and amalgams, Keller-Osserman conditions for diffusion-type operators on Riemannian manifolds, Ricci curvature and Betti numbers, Analysis of the Laplacian on a complete Riemannian manifold, Heat equation and compactifications of complete Riemannian manifolds, The Banach manifold structure of the space of metrics on noncompact manifolds, Riemannian manifolds whose Laplacians have purely continuous spectrum, Critical Riemannian 4-manifolds, Boundary estimates for the Ricci flow, Compactness of conformally compact Einstein manifolds in dimension 4, Geometric bounds on the growth rate of null-controllability cost for the heat equation in small time, The Dirichlet-to-Neumann map, viscosity solutions to eikonal equations, and the self-dual equations of pattern formation, Polynomial growth harmonic functions on complete Riemannian manifolds, A heat kernel lower bound for integral Ricci curvature, A note on Finsler version of Calabi-Yau theorem, \(K\)-homology classes of elliptic uniform pseudodifferential operators, Conformal tori with almost non-negative scalar curvature, An equivariant Atiyah-Patodi-Singer index theorem for proper actions. II: The \(K\)-theoretic index, On four-dimensional steady gradient Ricci solitons that dimension reduce, Parabolic Harnack inequality for divergence form second order differential operators, New features of the first eigenvalue on negatively curved spaces, Mean convex properly embedded \([ \varphi , \vec{e}_3 \)-minimal surfaces in \(\mathbb{R}^3\)], Lower bounds on \(\| K^ n \|_{1\to \infty}\) for some contractions \(K\) of \(L^ 2 (\mu)\), with applications to Markov operators, Analysis on geodesic balls of sub-elliptic operators, Multipliers for a distinguished Laplacean on solvable extensions of \(H\)-type groups, First order Feynman-Kac formula, Spectral multipliers on exponentially locally doubling metric measure spaces, Smoothing Riemannian metrics with Ricci curvature bounds, A note on the Bonnet-Myers theorem, Volume growth on manifolds with quadratic curvature decay and its applications, Boundedness of spectral multipliers of generalized Laplacians on compact manifolds with boundary, Propagation of singularities for subelliptic wave equations, Sobolev embeddings with weights in complete Riemannian manifolds, Rigidity of \(\kappa \)-noncollapsed steady Kähler-Ricci solitons, Scattering theory without injectivity radius assumptions, and spectral stability for the Ricci flow, Local Hardy spaces of differential forms on Riemannian manifolds, Mean curvature flow of area decreasing maps between Riemann surfaces, Hardy spaces and regularity for the inhomogeneous Dirichlet and Neumann problems, Volume comparison for hypersurfaces in Lorentzian manifolds and singularity theorems, Compactness of conformally compact Einstein 4-manifolds. II, Space of Ricci flows. II. Part B: Weak compactness of the flows, Some Cheeger-Gromov-Taylor type compactness theorems via \(m\)-Bakry-Émery and \(m\)-modified Ricci curvatures, The effects of self-interaction on constructing relativistic point particles, On the uniformly proper classification of open manifolds, Sharp geometric inequalities for closed hypersurfaces in manifolds with nonnegative Ricci curvature, Ricci flow under local almost non-negative curvature conditions, Hypersymplectic 4-manifolds, the \(G_2\)-Laplacian flow, and extension assuming bounded scalar curvature, On Sobolev norms for Lie group representations, Heat kernel on Ricci shrinkers, Delocalized \(L^2\)-invariants, Precompactness of solutions to the Ricci flow in the absence of injectivity radius estimates, \(L^p\)-boundedness of oscillating spectral multipliers on Riemannian manifolds, Poincaré-type inequalities and reconstruction of Paley-Wiener functions on manifolds, Functional inequalities for empty essential spectrum, Convergence of Riemannian 4-manifolds with \(L^2\)-curvature bounds, Volume growth, Green's functions, and parabolicity of ends, Equidistribution of holonomy about closed geodesics, Graphical mean curvature flow, Weakly PIC1 manifolds with maximal volume growth, A note on compactness theorems for the Bakry-Émery Ricci tensor and generalized quasi-Einstein tensors, Sobolev spaces adapted to the Schrödinger operator with inverse-square potential, Volume growth of Finsler manifolds with integral Ricci curvature bound, Ricci flow of regions with curvature bounded below in dimension three, Think globally, fit locally under the manifold setup: asymptotic analysis of locally linear embedding, Generalizations of Bonnet-Myers theorem on Finsler manifolds, A compactness theorem in Riemannian manifolds, On the asymptotic behavior of expanding gradient Ricci solitons, Controllability cost of conservative systems: resolvent condition and transmutation, Solvability of minimal graph equation under pointwise pinching condition for sectional curvatures, Bach-flat asymptotically locally Euclidean metrics, Stability results for Harnack inequalities., Some compactness theorems via \(m\)-Bakry-Émery and \(m\)-modified Ricci curvatures with negative \(m\), Asymptotics of class numbers, Local mollification of Riemannian metrics using Ricci flow, and Ricci limit spaces, A multiplier theorem for sub-Laplacians with drift on Lie groups, Brownian bridges to submanifolds, Gravitational instantons with faster than quadratic curvature decay. III., Spectral multipliers via resolvent type estimates on non-homogeneous metric measure spaces, A conformally invariant gap theorem characterizing \(\mathbb{CP}^2\) via the Ricci flow, Comparison theorems on Riemannian-Finsler manifolds with curvature quartic decay and their applications, Counterexamples to the \(L^p\)-Calderón-Zygmund estimate on open manifolds, Gravitating vortices with positive curvature, Wildly perturbed manifolds: norm resolvent and spectral convergence, Spectrum, harmonic functions, and hyperbolic metric spaces, Kähler manifolds with almost nonnegative curvature, On certain new means generated by generalized trigonometric functions, Multilinear spectral multipliers on Lie groups of polynomial growth, Perelman's functionals on cones. Construction of type III Ricci flows coming out of cones, Gaussian upper bounds for the heat kernels of some second-order operators on Riemannian manifolds, Geometric measure theory and manifolds of nonnegative Ricci curvature, On the generalized Becker-Stark type inequalities, Wave propagation speed on fractals, Semiclassical asymptotics, gauge fields, and quantum chaos, On a construction of coordinates at infinity on manifolds with fast curvature decay and maximal volume growth, Local Riesz transform and local Hardy spaces on Riemannian manifolds with bounded geometry, \(m\)-Bakry-Émery Ricci curvatures, Riccati inequalities, and bounded diameters, Myers-type compactness theorem with the Bakry-Emery Ricci tensor, Small-time asymptotics of hypoelliptic heat kernels near the diagonal, nilpotentization and related results, Ollivier Ricci curvature for general graph Laplacians: heat equation, Laplacian comparison, non-explosion and diameter bounds, A prime geodesic theorem for \(\mathrm{SL}_3(\mathbb{Z})\), The spectral bound and principal eigenvalues of Schrödinger operators on Riemannian manifolds, Asymptotics of finite energy monopoles on AC 3-manifolds, Some new results on eigenvectors via dimension, diameter, and Ricci curvature, Extensions of Bonnet-Myers-type theorems with the Bakry-Emery Ricci curvature, Noncollapsed degeneration of Einstein 4-manifolds. I, Plancherel-type estimates and sharp spectral multipliers, Small curvature concentration and Ricci flow smoothing, Riemann-Roch-Grothendieck and torsion for foliations, Weak-type endpoint bounds for Bochner-Riesz means for the Hermite operator, Superconnections and higher index theory, On the Perelman's reduced entropy and Ricci flat manifolds with maximal volume growth, An extension of Bonnet-Myers theorem, Sharp bounds for cumulative distribution functions, Evolving hypersurfaces by their mean curvature in the background manifold evolving by Ricci flow, Hitchin-Thorpe inequality for noncompact Einstein 4-manifolds, Convergence of riemannian manifolds with integral bounds on curvature. I, Optimal estimates of the heat kernel on cuspidal varieties, Cyclic cocycles, renormalization and eta-invariants, Poisson equation on some complete noncompact manifolds, A Concentration-Collapse Decomposition forL2Flow Singularities, Minimal Graphic Functions on Manifolds of Nonnegative Ricci Curvature, Fractional Brownian fields over manifolds, Resolvent and Spectral Measure on Non-Trapping Asymptotically Hyperbolic Manifolds II: Spectral Measure, Restriction Theorem, Spectral Multipliers, Estimations $L^p$ des fonctions du Laplacien sur les variétés cuspidales, Lower bound of Ricci flow's existence time, Asymptotics of relative heat traces and determinants on open surfaces of finite area, Collapsing irreducible 3-manifolds with nontrivial fundamental group, Short-time heat content asymptotics via the wave and eikonal equations, A Myers-type compactness theorem by the use of Bakry-Emery Ricci tensor, Riesz means on symmetric spaces, Riesz means on Lie groups and riemannian manifolds of nonnegative curvature, Relative entanglement entropy for widely separated regions in curved spacetime, Operational calculus and integral transforms for groups with finite propagation speed, Theorie du Potentiel sur les Graphes et les Varietes, Transgressed Euler classes of ${\rm SL}(2n,\mathbf{Z})$ vector bundles, adiabatic limits of eta invariants and special values of $L$-functions, Collapsing in the Einstein flow, Manifolds with Boundary and of Bounded Geometry, A gap theorem on complete shrinking gradient Ricci solitons, Heat kernel and Riesz transform of Schrödinger operators, Complete gradient expanding Ricci solitons with finite asymptotic scalar curvature ratio, Modular nuclearity: a generally covariant perspective, Monotonicity and complete monotonicity of some functions involving the modified Bessel functions of the second kind, On the existence of nonnegative solutions to semilinear differential inequality on Riemannian manifolds, On the Spectrum of Towers, \(L^{2}\)-invariants of Riemannian foliations, Asymptotic spectral flow, Boundedness of functional calculi of Schrödinger operators on generalized Lebesgue spaces \(L^{p(\cdot)}(\mathbb R^n)\), Geometry of Ricci solitons, Isometric immersions of \(\mathrm{RCD}(K, N)\) spaces via heat kernels, Variable Hardy spaces associated with operators satisfying Davies–Gaffney estimates on metric measure spaces of homogeneous type, Looking for compactness in Sobolev spaces on noncompact metric spaces, A Serre-Swan theorem for bundles of bounded geometry, Normalized Yamabe flow on manifolds with bounded geometry, Direct and Inverse Results on Bounded Domains for Meshless Methods via Localized Bases on Manifolds, An atomic decomposition of weighted Hardy spaces associated to self-adjoint operators, Collapsing with a lower bound on the curvature operator, Weighted \(L^p\) estimates for the area integral associated to self-adjoint operators, \(L^p\)-Liouville theorems on complete smooth metric measure spaces, The exponential map of a \(C^{1,1}\)-metric, On exponential observability estimates for the heat semigroup with explicit rates, Twistor spaces and the general adiabatic expansions, Adiabatic Limits, Nonmultiplicativity of Signature, and Leray Spectral Sequence, Volume growth and parabolicity, Scattering theory for the Laplacian on manifolds with bounded curvature, Non-singular solutions to the normalized Ricci flow equation, Mills' ratio: Monotonicity patterns and functional inequalities, On the volume growth of Kählerian manifolds with positive curvature near infinity, Weak type estimates for spherical multipliers on noncompact symmetric spaces, APS boundary conditions, eta invariants and adiabatic limits, A non-local flow for Riemann surfaces, Curvature estimates for the Ricci flow. I, A closed symplectic four-manifold has almost Kähler metrics of negative scalar curvature, A Convergence Theorem for Riemannian Submanifolds, Ball Covering on Manifolds With Nonnegative Ricci Curvature Near Infinity, L^{𝑝} estimates on functions of Markov operators, Estimation optimale du gradient du semi-groupe de la chaleur sur le groupe de Heisenberg, Collapsing sequences of solutions to the Ricci flow on 3-manifolds with almost nonnegative curvature, Dixmier traces on noncompact isospectral deformations, The spectrum of Schrödinger operators with positive potentials in Riemannian manifolds, Functional inequalities for particle systems on Polish spaces, Local index theory over étale groupoids, Ricci Curvature Bounds and Einstein Metrics on Compact Manifolds, On the existence of solutions of Poisson equation and Poincaré-Lelong equation, Local estimate on convexity radius and decay of injectivity radius in a Riemannian manifold, Embolic aspects of black hole entropy, On open scattering channels for manifolds with ends, Sobolev Inequalities in Familiar and Unfamiliar Settings, On Complete Manifolds With Nonnegative Ricci Curvature, Heat kernel on smooth metric measure spaces with nonnegative curvature, Curvature and injectivity radius estimates for Einstein 4-manifolds, On manifolds with quadratic curvature decay, Spectral multipliers for the Kohn sublaplacian on the sphere in $\mathbb{C}^{n}$, On the simply connectedness of nonnegatively curved Kähler manifolds and applications, Hardy spaces associated to non-negative self-adjoint operators satisfying Davies-Gaffney estimates, Sum of squares manifolds: The expressibility of the Laplace-Beltrami operator on pseudo-Riemannian manifolds as a sum of squares of vector fields, Eigenfunctions of the Laplacian on rotationally symmetric manifolds, The $b$-pseudodifferential calculus on Galois coverings and a higher Atiyah-Patodi-Singer index theorem, Manifolds with quadratic curvature decay and slow volume growth, A sampling theorem on homogeneous manifolds, Moduli spaces of critical Riemannian metrics in dimension four, On Poincaré Type Inequalities, On the wave equation with a potential, On the essential spectrum of Schrödinger operators on Riemannian manifolds, Eigenvalue estimate on complete noncompact Riemannian manifolds and applications, Asymptotic behavior of positively curved steady Ricci solitons, Wave decay on manifolds with bounded Ricci tensor, and related estimates, Compactness of relatively isospectral sets of surfaces via conformal surgeries, The Calderón-Zygmund inequality and Sobolev spaces on noncompact Riemannian manifolds, Gravitational instantons from rational elliptic surfaces, WITTEN DEFORMATION FOR NONCOMPACT MANIFOLDS WITH BOUNDED GEOMETRY, The relative eta invariant for a pair of Dirac-type operators on non-compact manifolds, Finite propagation speed and kernel estimates for Schrödinger operators, Some applications of heat flow to Laplace eigenfunctions, On the Placement of an Obstacle so as to Optimize the Dirichlet Heat Content, Local derivative estimates for the heat equation coupled to the Ricci flow, A note on convergence of noncompact nonsingular solutions of the Ricci flow, Sharp Gaussian upper bounds for Schrödinger heat kernel on gradient shrinking Ricci solitons, Analytic torsion for log-Enriques surfaces and Borcherds product, Lower bound of Schrödinger operators on Riemannian manifolds, Absence of principal eigenvalues for higher rank locally symmetric spaces, Myers-type theorems via m-Bakry–Émery Ricci curvatures of quartic decays, Delta L'Hospital-, Laplace- and variable limit-type monotonicity rules on time scales, A local Sobolev inequality on Ricci flow and its applications, Approximate solutions to second-order parabolic equations: evolution systems and discretization, Pressure at infinity and strong positive recurrence in negative curvature, Floer theory and reduced cohomology on open manifolds, Logarithmic heat kernel estimates without curvature restrictions, Existence and uniqueness of \(S^1\)-invariant Kähler-Ricci solitons, Ricci flow under Kato-type curvature lower bound, Some New Simple Inequalities Involving Exponential, Trigonometric and Hyperbolic Functions, The isoperimetric problem on Riemannian manifolds via Gromov–Hausdorff asymptotic analysis, Some curvature estimates of Kähler-Ricci flow, Good Wannier bases in Hilbert modules associated to topological insulators, On the stability of the behavior of random walks on groups, Area comparison, superharmonic functions, and applications, \(L^p-L^q\) estimates for functions of the Laplace-Beltrami operator on noncompact symmetric spaces. III, On the relation between elliptic and parabolic Harnack inequalities, On the stability of the behavior of random walks on groups, Nonlinear waves on 3D hyperbolic space, Elliptic operators and covers of Riemannian manifolds, Sobolev solutions of parabolic equation in a complete riemannian manifold, Boju–Funar type theorems via m-Bakry–Émery and m-modified Ricci curvatures, Renormalization of quantum field theory on Riemannian manifolds, A von Neumann Algebra Approach to Quantum Metrics/Quantum Relations, A von Neumann Algebra Approach to Quantum Metrics/Quantum Relations, On some aspects of oscillation theory and geometry, L’Hôpital’s monotone rule, Gromov’s theorem, and operations that preserve the monotonicity of quotients, Riesz transforms on a class of non-doubling manifolds, Reproducing kernel Hilbert spaces on manifolds: Sobolev and diffusion spaces, Optimal Curvature Estimates for Homogeneous Ricci Flows, Comparison theorems on Riemannian–Finsler manifolds with curvature quadratic decay and their applications, Approximate solutions to second order parabolic equations. I: Analytic estimates, On the structure of almost Einstein manifolds, Two boundary rigidity results for holomorphic maps