Isoperimetric inequality from the poisson equation via curvature

Renjin Jiang, Pekka Koskela

Type: Article

Publication Date: 2012-05-11

Citations: 7

DOI: https://doi.org/10.1002/cpa.21405

View Publication

Locations

Communications on Pure and Applied Mathematics - View

Similar Works

Action	Title	Year	Authors
+	Gradient estimate for solutions to Poisson equations in metric measure spaces	2011	Renjin Jiang
+	Gradient Estimate for Solutions to Poisson Equations in Metric Measure Spaces	2011	Renjin Jiang
+ PDF Chat	Weak curvature conditions and functional inequalities	2007	John Lott Cédric Villani
+	Log-Sobolev inequalities for subelliptic operators satisfying a generalized curvature dimension inequality	2012	Fabrice Baudoin Michel Bonnefont
+	Log-Sobolev inequalities for subelliptic operators satisfying a generalized curvature dimension inequality	2011	Fabrice Baudoin Michel Bonnefont
+	Sharp Isoperimetric Inequalities and Model Spaces for Curvature-Dimension-Diameter Condition	2011	Emanuel Milman
+	Sharp Isoperimetric Inequalities and Model Spaces for Curvature-Dimension-Diameter Condition	2011	Emanuel Milman
+	The Sharp Sobolev Inequality on Metric Measure Spaces with Lower Ricci Curvature Bounds	2015	Angelo Profeta
+ PDF Chat	Sharp isoperimetric inequalities and model spaces for the Curvature-Dimension-Diameter condition	2015	Emanuel Milman
+	Weak curvature conditions and functional inequalities	2005	John Lott Cédric Villani
+	Log-Sobolev inequalities for subelliptic operators satisfying a generalized curvature dimension inequality	2011	Fabrice Baudoin Michel Bonnefont
+ PDF Chat	A generalized Trudinger–Moser inequality on a compact Riemannian surface	2017	Xiaobao Zhu
+	A generalized Trudinger-Moser inequality on a compact Riemannian surface	2016	Xiaobao Zhu
+	Isoperimetric inequalities, heat equation and geometric applications	1985	Pierre Bérard
+	Isoperimetric inequalities involving generalized mean curvature	2002	Sven Winklmann
+	Weak curvature conditions and Poincare inequalities	2005	John Lott Cédric Villani
+	Isoperimetry on manifolds with Ricci bounded below: overview of recent results and methods	2023	Marco Pozzetta
+	Isoperimetric Inequalities (Variable Curvature)	2006	Isaac Chavel
+	Isoperimetric Inequalities (Constant Curvature)	2006	Isaac Chavel
+ PDF Chat	Metric measure spaces with Riemannian Ricci curvature bounded from below	2014	Luigi Ambrosio Nicola Gigli Giuseppe Savaré

Works That Cite This (7)

Action	Title	Year	Authors
+ PDF Chat	A New Reversed Version of a Generalized Sharp Hölder's Inequality and Its Applications	2013	Jing-Feng Tian Ximei Hu
+	Isoperimetric inequality via Lipschitz regularity of Cheeger-harmonic functions	2013	Renjin Jiang Pekka Koskela Dachun Yang
+ PDF Chat	An analytic proof of the planar quantitative isoperimetric inequality	2015	Li Guohua Xinyu Zhao Zongqi Ding Renjin Jiang
+ PDF Chat	Characterizations of Sets of Finite Perimeter Using Heat Kernels in Metric Spaces	2016	Niko Marola Michele Miranda Nageswari Shanmugalingam
+	Gradient estimates for heat kernels and harmonic functions	2019	Thierry Coulhon Renjin Jiang Pekka Koskela Adam Sikora
+	Sobolev Spaces on Metric Measure Spaces: An Approach Based on Upper Gradients	2015	Juha Heinonen Pekka Koskela Nageswari Shanmugalingam Jeremy T. Tyson
+	Characterizations of sets of finite perimeter using the Ornstein-Uhlenbeck semigroup in the Gauss space	2021	Xiang-Yun Xie Yu Liu Haihui Wang

Works Cited by This (37)

Action	Title	Year	Authors
+	Nonlinear Potential Theory on Metric Spaces	2011	Anders Björn Jana Björn
+ PDF Chat	Elliptic Partial Differential Equations of Second Order	2001	David Gilbarg Neil S. Trudinger
+ PDF Chat	On the structure of spaces with Ricci curvature bounded below. I	1997	Jeff Cheeger Tobias Colding
+ PDF Chat	Ricci curvature for metric-measure spaces via optimal transport	2009	John Lott Cédric Villani
+	Elliptic PDE's in probability and geometry: Symmetry and regularity of solutions	2008	Xavier Cabré
+ PDF Chat	On the parabolic kernel of the Schrödinger operator	1986	Peter Li Shing Tung Yau
+ PDF Chat	Modulus and the Poincar� inequality on metric measure spaces	2003	Stephen Keith
+ PDF Chat	On local Poincaré via transportation	2007	Max‐K. von Renesse
+	Differential equations on riemannian manifolds and their geometric applications	1975	Sheng Yao Cheng Shing‐Tung Yau
+	Lipschitz continuity of Cheeger-harmonic functions in metric measure spaces	2003	Pekka Koskela Kai Rajala Nageswari Shanmugalingam