Conformally flat manifolds, Kleinian groups and scalar curvature

From MaRDI portal

Publication:1111167

Jump to:navigation, search

DOI10.1007/BF01393992zbMath0658.53038OpenAlexW2012486996MaRDI QIDQ1111167

Richard M. Schoen, Shing Tung Yau

Publication date: 1988

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/143558

zbMATH Keywords

scalar curvature Green function energy function conformally flat

Mathematics Subject Classification ID

Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Global Riemannian geometry, including pinching (53C20) Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60) Kleinian groups (aspects of compact Riemann surfaces and uniformization) (30F40) Algebraic topology on manifolds and differential topology (57R19)

Related Items

About the mass of certain second order elliptic operators, Metrics of constant scalar curvature on sphere bundles, Geometric inequalities on locally conformally flat manifolds, On conformal qc geometry, spherical qc manifolds and convex cocompact subgroups of \(\mathrm{Sp}{(n+1,1)}\), On De Giorgi's conjecture: recent progress and open problems, On nonnegatively curved hypersurfaces in \(\mathbb{H}^{n+1}\), Yamabe metrics of positive scalar curvature and conformally flat manifolds, Killing initial data on spacelike conformal boundaries, The critical asymptotics of scalar curvatures of the conformal complete metrics with negative curvature, Hardy inequalities and dynamic instability of singular Yamabe metrics, The best constant problem in the Sobolev embedding theorem for complete Riemannian manifolds, Some conformally flat spin manifolds, Dirac operators and automorphic forms, Local behavior of singular positive solutions of semilinear elliptic equations with Sobolev exponent, Proof of the positive mass conjecture, Limit sets of Kleinian groups and conformally flat Riemannian manifolds, Nonlocal curvature and topology of locally conformally flat manifolds, Hamiltonian reduction, the Einstein flow, and collapse of 3-manifolds, Asymptotic expansions and conformal covariance of the mass of conformal differential operators, Asymptotic behavior of solutions to the \(\sigma_{k}\)-Yamabe equation near isolated singularities, Betti and Tachibana numbers of compact Riemannian manifolds, \(L^p\)-vanishing results for conformally flat manifolds and submanifolds, Gap theorems for locally conformally flat manifolds, On the \(L^2\)-cohomology of a convex cocompact hyperbolic manifold, Evolution equations in Riemannian geometry, Aubin's lemma for the Yamabe constants of infinite coverings and a positive mass theorem, Four-dimensional Wess--Zumino--Witten actions, A construction of constant scalar curvature manifolds with Delaunay-type ends, A rigidity theorem for complete noncompact Bach-flat manifolds, Prescribing scalar and boundary mean curvature on the three dimensional half sphere, A fully nonlinear version of the Yamabe problem and a Harnack type inequality., Canonical contact forms on spherical CR manifolds, The Weyl functional near the Yamabe invariant, The second Yamabe invariant with singularities, Computations of the orbifold Yamabe invariant, The Hijazi inequality on conformally parabolic manifolds, Rigidity of complete noncompact bach-flat \(n\)-manifolds, Deforming three-manifolds with positive scalar curvature, A new mass for asymptotically flat manifolds, A multiplicity result for the Yamabe problem on \(S^n\), The Gauss-Bonnet-Chern mass of higher-codimension graphs, Wiener regularity for large solutions of nonlinear equations, Isolated singularities of solutions to the Yamabe equation, The Yamabe constant on noncompact manifolds, Invariance of the Nayatani metrics for Kleinian manifolds, The Yamabe problem on stratified spaces, The scalar-curvature problem on higher-dimensional spheres, The Yamabe problem on manifolds with boundary: Existence and compactness results, Constant scalar curvature metrics with isolated singularities, On optimal 4-dimensional metrics, Removable singularity of positive solutions for a critical elliptic system with isolated singularity, Rigidity of complete noncompact Riemannian manifolds with harmonic curvature, The local Yamabe constant of Einstein stratified spaces, Deformations of \(Q\)-curvature. I, On compact manifolds with harmonic curvature and positive scalar curvature, On the asymptotically Poincaré-Einstein 4-manifolds with harmonic curvature, Second Yamabe constant on Riemannian products, Some \(L^p\) rigidity results for complete manifolds with harmonic curvature, The deformation theory of anti-self-dual conformal structures, Some compact conformally flat manifolds with non-negative scalar curvature, Extremal domains on Hadamard manifolds, On local behavior of singular positive solutions to nonlocal elliptic equations, An equivalence of scalar curvatures on Hermitian manifolds, Positive mass theorem for some asymptotically hyperbolic manifolds, Yamabe flow and metrics of constant scalar curvature on a complete manifold, Curvature in special base conformal warped products, Uniformization of conformally flat hermitian surfaces, Existence and uniqueness to a fully nonlinear version of the Loewner-Nirenberg problem, The Binet-Legendre metric in Finsler geometry, Singular solutions of fractional order conformal Laplacians, Complete noncompact manifolds with harmonic curvature, Rigidity of noncompact complete manifolds with harmonic curvature, Extending Yamabe flow on complete Riemannian manifolds, Partial regularity of finite Morse index solutions to the Lane-Emden equation, Local estimate on singular solution to scalar curvature equation, Bach-flat asymptotically locally Euclidean metrics, Conformal metrics with prescribed fractional scalar curvature on conformal infinities with positive fractional Yamabe constants, Hyperbolic 4-manifolds and tesselations, Asymptotic symmetry and local behavior of solutions of higher order conformally invariant equations with isolated singularities, Positive solutions to Schrödinger equations and geometric applications, Existence of positive weak solutions for fractional Lane-Emden equations with prescribed singular sets, An approach to classical quantum field theory based on the geometry of locally conformally flat space-time, Scalar curvature and conformal geometry, Orthogonal complex structures on domains in \(\mathbb R^4\), A strong maximum principle for the Paneitz operator and a non-local flow for the \(\mathcal Q\)-curvature, On conformal deformations of metrics on \(S^n\), Almost Hermitian symmetric manifolds. I: Local twistor theory, On complete conformally flat submanifolds with nullity in Euclidean space, \(\text{U}(1)\)-decomposable self-dual manifolds, Positive mass theorem for the Paneitz-Branson operator, Bounded stability for strongly coupled critical elliptic systems below the geometric threshold of the conformal Laplacian, Influence of the mass on nodal solutions of nonlinear PDEs, Refined asymptotic estimates for conformal scalar curvature equation via moving sphere method, Existence of positive weak solutions with a prescribed singular set of semilinear elliptic equations, Solutions with high dimensional singular set, to a conformally invariant elliptic equation in \(\mathbb{R}^ 4\) and in \(\mathbb{R}^ 6\), Existence and convergence of positive weak solutions of \(-\Delta u=u^{n\over {n-2}}\) in bounded domains of \(\mathbb{R}^ n\), \(n\geq 3\), On the scalar curvature of self-dual manifolds, Compactness of conformal metrics with integral bounds on curvature, Metrics with nonnegative isotropic curvature, Singular sets of a class of locally conformally flat manifolds, Kleinian groups with small limit sets, New Existence Results For Singular Solutions Of Some Semilinear Elliptic Equations, The general relativistic constraint equations, Quasiconformal stability of Kleinian groups and an embedding of a space of flat conformal structures, Hardy-singular boundary mass and Sobolev-critical variational problems, Some properties of the Schouten tensor and applications to conformal geometry, Mathematical general relativity: A sampler, A \(\sigma_2\) Penrose inequality for conformal asymptotically hyperbolic 4-discs, Tachibana-type theorems and special holonomy, The Cauchy problems for Einstein metrics and parallel spinors, Convex-cocompactness of Kleinian groups and conformally flat manifolds with positive scalar curvature, Flat twistor spaces, conformally flat manifolds and four-dimensional field theory, Rigidity theorems of complete Kähler-Einstein manifolds and complex space forms, Q-Curvature on a Class of Manifolds with Dimension at Least 5, Boundary value problems for some fully nonlinear elliptic equations, Einstein manifolds with finite \(L^p\)-norm of the Weyl curvature, Large singular solutions for conformal \(Q\)-curvature equations on \(\mathbb{S}^n\), Singular Yamabe metrics by equivariant reduction, Existence theorems of the fractional Yamabe problem, Conformally flat Riemannian manifolds with finite \(L^p\)-norm curvature, \(L^2\) curvature pinching theorems and vanishing theorems on complete Riemannian manifolds, Mass functions of a compact manifold, On the prescribed scalar curvature problem with very degenerate prescribed functions, A contribution to the geometry in the large of conformal diffeomorphisms, On the topology of closed manifolds with quasi-constant sectional curvature, Positive scalar curvature with skeleton singularities, The Yamabe problem, Non-negative solutions to fractional Laplace equations with isolated singularity, Unnamed Item, Conformal scalar curvature equations on complete manifolds, The Sobolev inequality and the asymptotoc volume, On a conformal invariant of the Dirac operator on noncompact manifolds, On the Positive Mass Theorem for Closed Riemannian Manifolds, Unique isoperimetric foliations of asymptotically flat manifolds in all dimensions, Hardy-Sobolev inequalities with singularities on non smooth boundary. Part 2: influence of the global geometry in small dimensions, Local estimates for conformal \(Q\)-curvature equations, Moduli Spaces of Singular Yamabe Metrics, The effect of linear perturbations on the Yamabe problem, Singular solutions for the constant \(Q\)-curvature problem, A fully nonlinear version of the Yamabe problem on locally conformally flat manifolds with umbilic boundary, Uniformization of spherical \( CR\) manifolds, Scalar curvature on noncompact complete Riemannian manifolds, The Gauss-Bonnet-Chern mass for graphic manifolds, A five-dimensional Riemannian manifold with an irreducible \(\mathrm{SO}(3)\)-structure as a model of abstract statistical manifold, The optimal exponent in the embedding into the Lebesgue spaces for functions with gradient in the Morrey space, Some Remarks on the Geometry of a Class of Locally Conformally Flat Metrics, Arsove–Huber Theorem in Higher Dimensions, The Li-Yau-Hamilton inequality for Yamabe flow on a closed CR 3-manifold, A Paneitz-Branson type equation with Neumann boundary conditions, On \(n\)-superharmonic functions and some geometric applications, Prescribing Scalar Curvatures on the Conformal Classes of Complete Metrics with Negative Curvature, Estimates of the scalar curvature equation via the method of moving planes III, BOUNDEDNESS OF POSITIVE SOLUTIONS OF THE CONFORMAL SCALAR CURVATURE EQUATION AND POSITIVE SCALAR CURVATURE, On the elliptic equation Δ𝑢+𝑘𝑢-𝐾𝑢^{𝑝}=0 on complete Riemannian manifolds and their geometric applications, Dirac type operators for spin manifolds associated to congruence subgroups of generalized modular groups, Blowing-up solutions for the Yamabe equation, The second Yamabe invariant, Compactness for conformal metrics with constant \(Q\) curvature on locally conformally flat manifolds, On some conformally invariant fully nonlinear equations. II: Liouville, Harnack and Yamabe, Compactness and global estimates for the geometric Paneitz equation in high dimensions, Asymptotic symmetries for conformal scalar curvature equations with singularity, EXISTENCE ANDA PRIORIBOUNDS FOR ELECTROSTATIC KLEIN–GORDON–MAXWELL SYSTEMS IN FULLY INHOMOGENEOUS SPACES, On conformally flat manifolds with constant positive scalar curvature, Locally conformally flat manifolds with constant scalar curvature, On the negativity of Ricci curvatures of complete conformal metrics, Liouville theorem and isolated singularity of fractional Laplacian system with critical exponents, Scalar curvature and the relative capacity of geodesic balls, An analytic construction of singular solutions related to a critical Yamabe problem, Un théorème de la masse positive pour le problème de Yamabe en dimension paire, The Yamabe operator and invariants on octonionic contact manifolds and convex cocompact subgroups of \(F_{4(-20)}\), Local behavior of positive solutions of higher order conformally invariant equations with a singular set, Conformal Automorphisms and Conformally Flat Manifolds, Rigidity of Einstein metrics as critical points of some quadratic curvature functionals on complete manifolds, Stability of quadratic curvature functionals at product of Einstein manifolds, Incomplete Yamabe flows and removable singularities, The Cheeger constant of an asymptotically locally hyperbolic manifold and the Yamabe type of its conformal infinity, Yamabe equation on some complete noncompact manifolds, Locally conformally flat metrics on surfaces of general type, The concentrated solutions on the nonhomogeneous scalar curvature problem, Large solutions for Yamabe and similar problems on domains in Riemannian manifolds, Multi‐periodic eigensolutions to the Dirac operator and applications to the generalized Helmholtz equation on flat cylinders and on the n‐torus, On Huber-type theorems in general dimensions, Some rigidity properties for manifolds with constant \(k\)-curvature of modified Schouten tensor, Foliation of an asymptotically flat end by critical capacitors, $3$-manifolds with positive flat conformal structure, Infinite-time incompleteness of noncompact Yamabe flow, Clifford and harmonic analysis on cylinders and tori, Classification of singular radial solutions to the \(\sigma_k\) Yamabe equation on annular domains, Moduli spaces of critical Riemannian metrics in dimension four, Homogeneous \((Z(n), \text{SO}(2n, \mathbb C))\)-geometries and uniformization, Singularities of Nonlinear Elliptic Systems, Betti and Tachibana numbers, Weighted Poincaré inequality and rigidity of complete manifolds, Hypersurfaces in hyperbolic space with support function, Positive energy theorems in fourth-order gravity, On Yamabe constants of products with hyperbolic spaces, A positive energy theorem for fourth-order gravity, Asymptotic behavior of positive solutions of the equation complete riemannian manifold and positive scalar curvature, Rigidity of noncompact manifolds with cyclic parallel Ricci curvature, Elliptic problems with integral diffusion, The Gibbons-Hawking ansatz in generalized Kähler geometry, The mass of an asymptotically hyperbolic end and distance estimates, Qualitative properties of singular solutions to fractional elliptic equations, Another proof of the Yamabe conjecture for locally conformally flat manifolds, Asymptotic behavior of solutions to the Yamabe equation with an asymptotically flat metric, Multiplicity and Stability of the Pohozaev Obstruction for Hardy-Schrödinger Equations with Boundary Singularity, Qualitative properties of singular solutions to the fractional Yamabe problem, The Yamabe problem for distributional curvature, Gradient estimate for solutions of the equation \(\Delta_p v +av^q=0\) on a complete Riemannian manifold, Multiplicity of singular solutions to the fractional Yamabe problem on spheres, Schwarzschild Harmonic Path Planning and Tetrahedral Mesh Smoothing, Singular CR structures of constant Webster curvature and applications, Generalized soap bubbles and the topology of manifolds with positive scalar curvature, The heat kernel on asymptotically hyperbolic manifolds, Elliptic PDEs on Compact Ricci Limit Spaces and Applications, RIGIDITY OF COMPLETE RIEMANNIAN MANIFOLDS WITH VANISHING BACH TENSOR, The GBC mass for asymptotically hyperbolic manifolds, Extremals for Sobolev and Exponential Inequalities in Hyperbolic Space, Non-compactness and multiplicity results for the Yamabe problem on \(S^n\), On the negative case of the singular Yamabe problem, Homogeneous domains in the space of complex structures, Unnamed Item, On the negative case of the singular Yamabe problem, Nayatani’s metric and conformal transformations of a Kleinian manifold, Yamabe invariant for complete manifold with nonpositive scalar curvature., Multiplicity results for the Yamabe problem on S ⁿ , Some nonlinear elliptic equations from geometry, Conformal invariants and partial differential equations, Conformally invariant inequalities in domains in Euclidean space, Convergence of the fractional Yamabe flow for a class of initial data, The Yamabe invariant, L p -Green potential estimates on noncompact Riemannian manifolds

Cites Work

Retrieved from "https://portal.mardi4nfdi.de/w/index.php?title=Publication:1111167&oldid=13151567"