The Logarithmic Sobolev Inequality for a Submanifold in Euclidean Space

Simon Brendle

Type: Article

Publication Date: 2020-10-04

Citations: 11

DOI: https://doi.org/10.1002/cpa.21949

Abstract

Abstract We prove a sharp logarithmic Sobolev inequality that holds for submanifolds in Euclidean space of arbitrary dimension and codimension. Like the Michael‐Simon Sobolev inequality, this inequality includes a term involving the mean curvature. © 2020 Wiley Periodicals, Inc.

Locations

Communications on Pure and Applied Mathematics - View
arXiv (Cornell University) - View - PDF

Similar Works

Action	Title	Year	Authors
+	The logarithmic Sobolev inequality for a submanifold in Euclidean space	2019	Simon Brendle
+ PDF Chat	The Log-Sobolev Inequality for a Submanifold in Manifolds With Asymptotic Non-Negative Intermediate Ricci Curvature	2024	Jihye Lee Fabio Ricci
+ PDF Chat	Sobolev Inequalities in Manifolds with Nonnegative Curvature	2022	Simon Brendle
+	The logarithmic Sobolev inequality for a submanifold in manifold with nonnegative sectional curvature	2021	Chengyang Yi Yu Zheng
+ PDF Chat	$L^p$-Sobolev inequalities on Euclidean submanifolds	2024	Zoltán M. Balogh Alexandru Kristály Ágnes Mester
+	The Logarithmic Sobolev Inequality for a Submanifold in Manifolds with Nonnegative Sectional Curvature	2024	Chengyang Yi Yu Zheng
+ PDF Chat	Logarithmic-Sobolev inequalities on non-compact Euclidean submanifolds: sharpness and rigidity	2024	Zoltán M. Balogh Alexandru Kristály
+	A Logarithmic Sobolev Inequality for Closed Submanifolds with Constant Length of Mean Curvature Vector	2024	Doanh Pham
+	The logarithmic Sobolev inequality for a submanifold in manifolds with asymptotically nonnegative sectional curvature	2023	Yuxin Dong Hezi Lin Lingen Lu
+ PDF Chat	A logarithmic Sobolev inequality for closed submanifolds with constant length of mean curvature vector	2024	Doanh Pham
+	Logarithmic Sobolev inequalities on submanifolds of Euclidean space	2000	Klaus Ecker
+	The Log-Sobolev inequality for a submanifold in manifolds with asymptotic non-negative intermediate Ricci curvature	2023	Jihye Lee Fabio Ricci
+ PDF Chat	Optimal Transport Approach to Michael-Simon-Sobolev Inequalities in Manifolds with Intermediate Ricci Curvature Lower Bounds	2023	Kai-Hsiang Wang
+ PDF Chat	Logarithmic Harnack inequalities and differential Harnack estimates for p-Laplacian on Riemannian manifolds	2022	Yu‐Zhao Wang Yan Xue
+	Logarithmic Sobolev inequalities	1989	E. B. Davies
+	The isoperimetric inequality for a minimal submanifold in Euclidean space	2020	Simon Brendle
+	Classification of separable hypersurfaces with constant sectional curvature	2023	Muhittin Evren Aydın Rafael López Gabriel‐Eduard Vîlcu
+ PDF Chat	Sobolev inequality on manifolds with asymptotically nonnegative Bakry–Émery Ricci curvature	2024	Yuxin Dong Hezi Lin Lingen Lu
+	Sharp isoperimetric and Sobolev inequalities in spaces with nonnegative Ricci curvature	2020	Zoltán M. Balogh Alexandru Kristály
+	Explicit sharp constants in Sobolev inequalities on Riemannian manifolds with nonnegative Ricci curvature	2020	Alexandru Kristály

Works That Cite This (11)

Action	Title	Year	Authors
+ PDF Chat	The relative isoperimetric inequality for minimal submanifolds with free boundary in the Euclidean space	2023	Lei Liu Guofang Wang Liangjun Weng
+ PDF Chat	Minimal hypersurfaces and geometric inequalities	2023	Simon Brendle
+ PDF Chat	Isoperimetric problems for spacelike domains in generalized Robertson–Walker spaces	2020	Ben Lambert Julian Scheuer
+	The logarithmic Sobolev inequality for a submanifold in manifolds with asymptotically nonnegative sectional curvature	2023	Yuxin Dong Hezi Lin Lingen Lu
+	Geometry and Topology	2021	Bogdan Grechuk
+ PDF Chat	The Log-Sobolev Inequality for a Submanifold in Manifolds With Asymptotic Non-Negative Intermediate Ricci Curvature	2024	Jihye Lee Fabio Ricci
+	A Sharp Sobolev Principle on the Graphic Submanifolds of $${\mathbb {R}}^{n+m}$$	2024	Jie Xiao Fanheng Xu
+	Sobolev inequality and isoperimetric inequality for submanifolds in a smooth metric measure space	2023	Pak Tung Ho Juncheol Pyo
+	Some Geometric Inequalities by the ABP Method	2023	Doanh Pham
+	The Logarithmic Sobolev Inequality for a Submanifold in Manifolds with Nonnegative Sectional Curvature	2024	Chengyang Yi Yu Zheng

Works Cited by This (15)

Action	Title	Year	Authors
+	Elliptic PDE's in probability and geometry: Symmetry and regularity of solutions	2008	Xavier Cabré
+	The entropy formula for the Ricci flow and its geometric applications	2002	Grisha Perelman
+ PDF Chat	Asymptotic behavior for singularities of the mean curvature flow	1990	Gerhard Huisken
+	The Brunn-Minkowski inequality in Gauss space	1975	Christer Borell
+ PDF Chat	Extremal properties of half-spaces for spherically invariant measures	1978	V. N. Sudakov Boris Tsirelson
+ PDF Chat	Inequalities of the Brunn–Minkowski type for Gaussian measures	2007	Christer Borell
+	Submanifolds, isoperimetric inequalities and optimal transportation	2010	Philippe Castillon
+	Sobolev and mean‐value inequalities on generalized submanifolds of R<sup>n</sup>	1973	J. H. Michael L. Simon
+	Logarithmic Sobolev inequalities on submanifolds of Euclidean space	2000	Klaus Ecker
+	On the First Variation of a Varifold	1972	William K. Allard