Total curvature and the isoperimetric inequality in Cartan-Hadamard manifolds

DOI10.1007/s12220-021-00801-2zbMath1497.53076arXiv1908.09814OpenAlexW2969487649MaRDI QIDQ2074504

Mohammad Ghomi, Joel Spruck

Publication date: 10 February 2022

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1908.09814

zbMATH Keywords

cut locusconvex hullmedial axisquermassintegralsisoperimetric profileinf-convolutionsemiconcave functionspositive reachsigned distance function

Mathematics Subject Classification ID

Geometric measure and integration theory, integral and normal currents in optimization (49Q15) Elliptic equations on manifolds, general theory (58J05) Length, area, volume and convex sets (aspects of convex geometry) (52A38) Global Riemannian geometry, including pinching (53C20)

Related Items

Sharp Morrey–Sobolev inequalities and eigenvalue problems on Riemannian–Finsler manifolds with nonnegative Ricci curvature ⋮ Rigidity of nonpositively curved manifolds with convex boundary ⋮ Boundary regularity for anisotropic minimal Lipschitz graphs ⋮ Some functional properties on Cartan-Hadamard manifolds of very negative curvature ⋮ Total mean curvatures of Riemannian hypersurfaces ⋮ Curvature measures and soap bubbles beyond convexity

Cites Work

• Regularization by sup-inf convolutions on Riemannian manifolds: an extension of Lasry-Lions theorem to manifolds of bounded curvature
• Tangent cones and regularity of real hypersurfaces
• Continuity of the isoperimetric profile of a complete Riemannian manifold under sectional curvature conditions
• An extension of Alexandrov's theorem on second derivatives of convex functions
• Semiconcave functions, Hamilton-Jacobi equations, and optimal control
• On the total curvature of immersed manifolds. II
• A sharp four dimensional isoperimetric inequality
• The global medial structure of regions in \(\mathbb R^3\)
• Inf-convolution and regularization of convex functions on Riemannian manifolds of nonpositive curvature
• Nonlinear evolution by mean curvature and isoperimetric inequalities
• Mean curvature flow and isoperimetric inequalities. Edited by Vicente Miquel and Joan Porti
• Sur une inégalité isopérimétrique qui généralise celle de Paul Lévy-Gromov. (On an isoperimetric inequality which generalizes that of Paul Lévy-Gromov)
• Manifolds of nonpositive curvature
• Asymptotic theory of finite dimensional normed spaces. With an appendix by M. Gromov: Isoperimetric inequalities in Riemannian manifolds
• The Dirichlet problem for nonlinear second order elliptic equations. III: Functions of the eigenvalues of the Hessian
• Geometry of horospheres
• Sets with positive reach
• Minimal boundaries enclosing a given volume
• Monotonicity of integral Gauss curvature
• An isoperimetric comparison theorem
• Integrals of subharmonic functions on manifolds of nonnegative curvature
• \(C^\infty\) convex functions and manifolds of positive curvature
• Local and global convexity in complete Riemannian manifolds
• Total curvatures of convex hypersurfaces in hyperbolic space
• Area minimizing sets subject to a volume constraint in a convex set
• Blaschke's rolling theorem for manifolds with boundary
• On soap bubbles and isoperimetric regions in non-compact symmetric spaces. I
• Intrinsic curvatures in analytic-geometric categories
• Strictly convex submanifolds and hypersurfaces of positive curvature.
• New geometric aspects of Moser-Trudinger inequalities on Riemannian manifolds: the non-compact case
• The volume of a small geodesic ball of a Riemannian manifold
• Hamilton-Jacobi equations and distance functions on Riemannian manifolds
• Stability and finiteness properties of medial axis and skeleton
• Regularity of \(C^ 1\) solutions of the Hamilton-Jacobi equation.
• Isoperimetric inequalities for quermassintegrals
• Remarks on manifolds with two-sided curvature bounds
• Geometry of isoparametric hypersurfaces in Riemannian manifolds
• Harmonic mean curvature flow and geometric inequalities
• Optimal isoperimetric inequalities for surfaces in any codimension in Cartan-Hadamard manifolds
• The Cartan-Hadamard conjecture and the little prince
• The relative isoperimetric inequality outside convex domains in \(\mathbb{R}^{n}\)
• Controlled Markov processes and viscosity solutions
• A new 3-dimensional curvature integral formula for PL-manifolds of non-positive curvature
• Total positive curvature of hypersurfaces with convex boundary
• Constant mean curvature hypersurfaces condensing on a submanifold
• Sharp Morrey-Sobolev inequalities on complete Riemannian manifolds
• Schnittort und konvexe Mengen in vollständigen Riemannschen Mannigfaltigkeiten
• Normal and integral currents
• On the structure of complete manifolds of nonnegative curvature
• On the Hessian of a function and the curvature of its graph
• Isoperimetrische Ungleichungen für Bereiche auf Flächen
• Some sharp isoperimetric theorems for Riemannian manifolds
• The Isoperimetric Problem on Surfaces
• On the total curvature of convex hypersurfaces in hyperbolic spaces
• Convex analysis and optimization in Hadamard spaces
• Sets of Finite Perimeter and Geometric Variational Problems
• Shapes and Geometries
• The distance function to the boundary, Finsler geometry, and the singular set of viscosity solutions of some Hamilton-Jacobi equations
• On the Total Curvature of Immersed Manifolds
• Curvature Measures
• Shorter Notes: Regularity of the Distance Function
• The relative isoperimetric inequality in Cartan-Hadamard 3-manifolds
• Local Rigidity of Symmetric Spaces of Nonpositive Curvature
• Blaschke’s rolling theorem in 𝑅ⁿ
• Differential geometry of geodesic spheres.
• Sobolev and isoperimetric inequalities for riemannian submanifolds
• Isoperimetric constants and the first eigenvalue of a compact riemannian manifold
• Analytische Eigenschaften konvexer Funktionen auf Riemannschen Mannigfaltigkeiten.
• The isoperimetric inequality
• Best constants in Sobolev inequalities for compact manifolds of nonpositive curvature
• Sign and geometric meaning of curvature
• Variational Analysis
• VOLUME ESTIMATE VIA TOTAL CURVATURE IN HYPERBOLIC SPACES
• A Panoramic View of Riemannian Geometry
• Regularity of isoperimetric hypersurfaces in Riemannian manifolds
• Sharp local isoperimetric inequalities involving the scalar curvature
• Dido's Problem and Its Impact on Modern Mathematics
• On Hypersurfaces of Hyperbolic Space Infinitesimally Supported by Horospheres
• Inequalities of Gauss-Bonnet Type for a Convex Domain
• Subharmonic Functions and Surfaces of Negative Curvature
• The 𝐴𝐵 program in geometric analysis: sharp Sobolev inequalities and related problems
• Sharp Isoperimetric Inequalities for Small Volumes in Complete Noncompact Riemannian Manifolds of Bounded Geometry Involving the Scalar Curvature
• Horoball Hulls and Extents in Positive Definite Space
• The Isoperimetric Problem
• Sobolev spaces on manifolds
• Convex Bodies The Brunn-MinkowskiTheory
• Existence of C1,1C1,1 critical sub-solutions of the Hamilton–Jacobi equation on compact manifolds
• Curvatures of typical convex bodies— the complete picture
• The Total Absolute Curvature of Immersed Manifolds
• Isoperimetric Inequalities and Their Applications
• Manifolds of Negative Curvature
• Isoperimetric Inequalities in Mathematical Physics. (AM-27)
• Convex analysis and monotone operator theory in Hilbert spaces
• Metric structures for Riemannian and non-Riemannian spaces. Transl. from the French by Sean Michael Bates. With appendices by M. Katz, P. Pansu, and S. Semmes. Edited by J. LaFontaine and P. Pansu
• Riemannian geometry and geometric analysis
• Higher eigenvalues and isoperimetric inequalities on Riemannian manifolds and graphs
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