Sobolev and isoperimetric inequalities for riemannian submanifolds

From MaRDI portal
Publication:4048193

DOI10.1002/cpa.3160270601zbMath0295.53025OpenAlexW2131183115WikidataQ115406214 ScholiaQ115406214MaRDI QIDQ4048193

Joel Spruck, David A. Hoffman

Publication date: 1974

Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/cpa.3160270601



Related Items

Isoperimetric inequalities for Riemannian products, Schrödinger-Maxwell systems on non-compact Riemannian manifolds, Rigidity theorem for Willmore surfaces in a sphere, Harmonic \(p\)-forms on Hadamard manifolds with finite total curvature, \(L^p\;p\)-harmonic 1-forms on submanifolds in a Hadamard manifold, Some geometric inequalities for varifolds on Riemannian manifolds based on monotonicity identities, Sobolev inequalities on forms and \(L^{p,q}\)-cohomology on complete Riemannian manifolds, Total curvature and \(L ^{2}\) harmonic 1-forms on complete submanifolds in space forms, Vanishing theorems for \(L^{2}\) harmonic forms on complete Riemannian manifolds, Rigidity of stable marginally outer trapped surfaces in initial data sets, Minimal hypersurfaces in \(\mathbb {H}^n \times \mathbb {R}\), total curvature and index, Isoperimetric inequalities, isometric actions and the higher Newman numbers, Inverse mean curvature flows in warped product manifolds, Sobolev inequality and stability of minimal submanifolds, Eigenvalue estimate and gap theorems for submanifolds in the hyperbolic space, On-diagonal lower bounds for heat kernels and Markov chains, Curvature estimates for minimal hypersurfaces in singular spaces, Minimising hulls, p-capacity and isoperimetric inequality on complete Riemannian manifolds, Spectral convergence of Riemannian manifolds. II, Characterization of Whitney spheres among Lagrangian submanifolds with conformal Maslov form, Riesz transforms for symmetric diffusion operators on complete Riemannian manifolds, On the stability operator of submanifolds with constant mean curvature in hyperbolic space, Upper bounds for the first eigenvalue of the Laplacian of hypersurfaces in terms of anisotropic mean curvatures, On stable constant mean curvature hypersurfaces, Remarks on mean curvature flow solitons in warped products, Isometry-invariant solutions to a critical problem on non-compact Riemannian manifolds, On the structure of submanifolds in Euclidean space with flat normal bundle, Improved local well-posedness for quasilinear wave equations in dimension three, Geometric characterizations of asymptotic flatness and linear momentum in general relativity, \(C^{1,\alpha}\)-regularity for surfaces with \(H\in L^p\), Finiteness of non-parabolic ends on submanifolds in spheres, Sobolev and isoperimetric inequalities for submanifolds in weighted ambient spaces, Complete submanifolds of manifolds of negative curvature, Remarks on mean-value inequalities on \(m\)-dimensional submanifolds of \(S^n\), Bubble tree convergence for harmonic maps into compact locally CAT(1) spaces, Surgery of the Faber-Krahn inequality and applications to heat kernel bounds, Smoothing effects for the porous medium equation on Cartan-Hadamard manifolds, \(L^{2}\) harmonic 2-forms on minimal hypersurfaces in spheres, Certain inequalities for mean curvature, area, and volume in a Riemannian manifold, On nonlinear Schrödinger equations on the hyperbolic space, Spectral convergence of conformally immmersed surfaces with bounded mean curvature, Isoperimetric inequalities for submanifolds with bounded mean curvature, Convergence of Lagrangian mean curvature flow in Kähler-Einstein manifolds, Eigenvalue pinching and application to the stability and the almost umbilicity of hypersurfaces, Limits of minimal surfaces and Scherk's fifth surface, The structure of weakly stable constant mean curvature hypersurfaces, \(L^2\)-harmonic 1-forms on submanifolds with finite total curvature, Vanishing theorems for \(L^2\) harmonic 1-forms on complete submanifolds in a Riemannian manifold, The extension for mean curvature flow with finite integral curvature in Riemannian manifolds, An exact sequence in \(L^2\)-cohomology, Vanishing theorem for \(p\)-harmonic 1-forms on complete submanifolds in spheres, CMC biconservative surfaces in \(\mathbb S^n\times\mathbb R\) and \(\mathbb H^n\times\mathbb R\), Volumes and intrinsic diameters of hypersurfaces, On the reduced \(L^2\) cohomology on complete hypersurfaces in Euclidean spaces, \(L^2\) harmonic forms on submanifolds in a Hadamard manifold, Diameter of an immersed surface with boundary, \(p\)-harmonic \(l\)-forms on complete noncompact submanifolds in sphere with flat normal bundle, Minimal graphs and graphical mean curvature flow in \(M^n\times \mathbb{R} \), Constant mean curvature surfaces in \({\mathbb {M}}^2(c)\times \mathbb {R}\) and finite total curvature, Rigidity of complete minimal hypersurfaces in the Euclidean space, \(L^p\) harmonic 1-forms on minimal hypersurfaces with finite index, Pinching of the first eigenvalue for second order operators on hypersurfaces of the Euclidean space, Rigidity of complete minimal submanifolds in a hyperbolic space, \(\varepsilon_0\)-regularity for mean curvature flow from surface to flat Riemannian manifold, On the structure of submanifolds in the hyperbolic space, The gap phenomenon for extremal submanifolds in a sphere, Uniform decay estimates for finite-energy solutions of semi-linear elliptic inequalities and geometric applications, Caccioppoli's inequalities on constant mean curvature hypersurfaces in Riemannian manifolds, An isoperimetric comparison theorem, A finiteness theorem for ends of complete manifolds supporting a Sobolev type inequality, Remarks on the stability of minimal submanifolds of \(\mathbb R^n\), \(L^{2}\) harmonic 1-forms on minimal submanifolds in spheres, A gap theorem on submanifolds with finite total curvature in spheres, Submanifolds, isoperimetric inequalities and optimal transportation, Uniform decay estimates for solutions of the Yamabe equation, Isoperimetric problems for spacelike domains in generalized Robertson-Walker spaces, Bernstein-Heinz-Chern results in calibrated manifolds, Deforming hypersurfaces of the sphere by their mean curvature, \(L^{2}\) harmonic 1-forms on minimal submanifolds in hyperbolic space, Hardy and Rellich inequalities for submanifolds in Hadamard spaces, Positive solutions to Schrödinger equations and geometric applications, \(p\)-harmonic \(\ell\)-forms on Riemannian manifolds with a weighted Poincaré inequality, The \(p\)-hyperbolicity of infinity volume ends and applications, Stability properties and topology at infinity of \(f\)-minimal hypersurfaces, Survey on the asymptotic Dirichlet problem for the minimal surface equation, The Feller property on Riemannian manifolds, Stable minimal hypersurfaces in a Riemannian manifold with pinched negative sectional curvature, Total curvature and the isoperimetric inequality in Cartan-Hadamard manifolds, The behaviour of the mean curvature flow for pinched submanifolds in rank one symmetric spaces, The mean curvature and volume growth of complete noncompact submanifolds, Existence and uniqueness of constant mean curvature foliation of asymptotically hyperbolic 3-manifolds, Willmore type inequality using monotonicity formulas, Complete submanifolds with bounded mean curvature in a Hadamard manifold, On heat kernel comparison theorems, An isoperimetric inequality and the first Steklov eigenvalue, The real Schwarz Lemma and geometric applications, Length and speed of a string in a geodesic surface, Schrödinger equation on Cartan-Hadamard manifolds with oscillating nonlinearities, Contracting convex hypersurfaces in Riemannian manifolds by their mean curvature, Multiple solutions to the Plateau problem for nonconstant mean curvature, Vanishing properties of $p$-harmonic $\ell$-forms on Riemannian manifolds, Isoperimetric type inequalities on submanifolds in rotation-symmetric spaces, Penrose type inequalities for asymptotically hyperbolic graphs, Quantitative index bounds for translators via topology, Weighted volume growth and vanishing properties of \(f\)-minimal hypersurfaces in a weighted manifold, VANISHING THEOREMS FOR HYPERSURFACES IN THE UNIT SPHERE, \(L^{p}\) harmonic 1-forms on submanifolds in spheres, Gap theorems for minimal submanifolds of a hyperbolic space, Evolving hypersurfaces by their mean curvature in the background manifold evolving by Ricci flow, Dirichlet problem at infinity for \(\mathcal A\) -harmonic functions, Dark energy from topology, An application of Moser iteration to complete minimal submanifolds in a sphere, Gap theorems for complete \(\lambda\)-hypersurfaces, On the $1/H$-flow by $p$-Laplace approximation: new estimates via fake distances under Ricci lower bounds, The topological structure of complete noncompact submanifolds in spheres, \(p\)-harmonic functions and connectedness at infinity of complete submanifolds in a Riemannian manifold, An eigenvalue pinching theorem for compact hypersurfaces in a sphere, New stability results for spheres and Wulff shapes, Rigidity and vanishing theorems for complete translating solitons, p-harmonic 1-forms on totally real submanifolds in complex space forms, On energy gap phenomena of the Whitney spheres in \(\mathbb{C}^n\) or \(\mathbb{CP}^n\), On the volume of locally conformally flat 4-dimensional closed hypersurface, Some rigidity results of minimal submanifolds in space forms, Some functional properties on Cartan-Hadamard manifolds of very negative curvature, Weighted monotonicity theorems and applications to minimal surfaces of ℍⁿ and 𝕊ⁿ, The extension and convergence of mean curvature flow in higher codimension, harmonic 1-forms on hypersurfaces with finite index, Diameter estimates for submanifolds in manifolds with nonnegative curvature, Mean curvature flow of arbitrary codimension in complex projective spaces, Harmonic 1-forms on minimal hypersurfaces in \(\mathbb{S}^n \times \mathbb{R}\), On the nonlinear Schrödinger equation on the Poincaré ball model, The complete hyper-surfaces with zero scalar curvature in \(\mathbb{R}^{n+1}\), A note about a Caffarelli-Kohn-Nirenberg type inequality for Euclidean submanifolds, Isoperimetric properties of the mean curvature flow, Rigidity results and topology at infinity of translating solitons of the mean curvature flow, Stable complete surfaces with constant mean curvature, Unnamed Item, A generalization of Pólya conjecture and Li-Yau inequalities for higher eigenvalues, Gap theorems for submanifolds in \(\mathbb{H}^n\times\mathbb{R}\), \(L^2\)-isolation phenomenon for complete surfaces arising from Yang-Mills theory, Lower bounds for the first eigenvalues of the p-Laplacian and the weighted p-Laplacian, Isoperimetric constants and the first eigenvalue of a compact riemannian manifold, Quadratically pinched hypersurfaces of the sphere via mean curvature flow with surgery, Extrinsic radius pinching for hypersurfaces of space forms, Upper bounds for the first non-zero Steklov eigenvalue via anisotropic mean curvatures, A remark on the Sobolev inequality for Riemannian submanifolds, Higher-order Sobolev embeddings and isoperimetric inequalities, Rigidity of minimal submanifolds in space forms, A Convergence Theorem for Riemannian Submanifolds, A NEW RESULT ABOUT ALMOST UMBILICAL HYPERSURFACES OF REAL SPACE FORMS, Existence and Blow-Up Behavior for Solutions of the Generalized Jang Equation, Rigidity of minimal submanifolds in hyperbolic space, Unnamed Item, Vanishing theorems for \(L^2\) harmonic forms on complete submanifolds in Euclidean space, Harmonic 1-forms on immersed hypersurfaces in a Riemannian manifold with weighted bi-Ricci curvature bounded from below, Estimates for the Energy Integral of Quasiregular Mappings on Riemannian Manifolds and Isoperimetry, Total scalar curvature and rigidity of minimal hypersurfaces in Euclidean space, Higher-order geometric flow of hypersurfaces in a Riemannian manifold, Submanifolds with parallel Gaussian mean curvature vector in Euclidean spaces, Volume Growth and Escape Rate of Brownian Motion on a Cartan—Hadamard Manifold, ON ALMOST STABLE CMC HYPERSURFACES IN MANIFOLDS OF BOUNDED SECTIONAL CURVATURE, On reduced L2 cohomology of hypersurfaces in spheres with finite total curvature, Optimal isoperimetric inequalities for surfaces in any codimension in Cartan-Hadamard manifolds, \(L^p\) harmonic 1-forms on totally real submanifolds in a complex projective space, The \(p\)-eigenvalue estimates and \(L^q\)\( p\)-harmonic forms on submanifolds of Hadamard manifolds, The Abresch–Rosenberg shape operator and applications, The non-parabolicity of infinite volume ends, The weighted Sobolev and mean value inequalities, Analysis of weighted p-harmonic forms and applications, Volume growth of submanifolds and the Cheeger isoperimetric constant, Banach algebras of weakly differentiable functions, Some characterizations of space-forms, Escape rate of brownian motion on riemanian manifolds, Isoperimetric inequalities under bounded integral norms of Ricci curvature and mean curvature, On complete hypersurfaces with constant mean curvature and finite \(L^p\)-norm curvature in \(\mathbb R^{n+1}\), Vanishing theorems on Riemannian manifolds, and geometric applications, L 2 harmonic forms and finiteness of ends, Universal Hardy–Sobolev inequalities on hypersurfaces of Euclidean space, On the structure and volume growth of submanifolds in Riemannian manifolds, Gap theorems on hypersurfaces in spheres, The Calderón-Zygmund inequality and Sobolev spaces on noncompact Riemannian manifolds



Cites Work