Rectifiability of singular sets of noncollapsed limit spaces with Ricci curvature bounded below

2021 ◽  
Vol 193 (2) ◽  
pp. 407
Author(s):  
Cheeger ◽  
Jiang ◽  
Naber
Keyword(s):  
Ricci Curvature ◽  
Singular Sets ◽  
Bounded Below

A note on Ricci flow with Ricci curvature bounded below

2017 ◽  
Vol 2017 (726) ◽  
Author(s):  
Xiuxiong Chen ◽  
Fang Yuan
Keyword(s):  
Ricci Curvature ◽  
Ricci Flow ◽  
Ricci Flows ◽  
Bounded Below

AbstractIn this note, we will prove that given a sequence of Ricci flows

Gradient Estimates for Harmonic Functions on Manifolds With Lipschitz Metrics

1998 ◽  
Vol 50 (6) ◽  
pp. 1163-1175 ◽  
Author(s):  
Jingyi Chen ◽  
Elton P. Hsu
Keyword(s):  
Ricci Curvature ◽  
Harmonic Functions ◽  
Volume Growth ◽  
Gradient Estimate ◽  
Gradient Estimates ◽  
Smooth Manifolds ◽  
Lipschitz Continuous ◽  
Bounded Below

AbstractWe introduce a distributional Ricci curvature on complete smooth manifolds with Lipschitz continuous metrics. Under an assumption on the volume growth of geodesics balls, we obtain a gradient estimate for weakly harmonic functions if the distributional Ricci curvature is bounded below.

scholarly journals A Note on Finsler Version of Calabi-Yau Theorem

2018 ◽  
Vol 2018 ◽  
pp. 1-4
Author(s):  
Songting Yin ◽  
Ruixin Wang ◽  
Pan Zhang
Keyword(s):  
Ricci Curvature ◽  
Volume Growth ◽  
Finsler Manifold ◽  
Infinite Volume ◽  
Growth Theorem ◽  
Negative Function ◽  
Weighted Ricci Curvature ◽  
Bounded Below

We generalize Calabi-Yau’s linear volume growth theorem to Finsler manifold with the weighted Ricci curvature bounded below by a negative function and show that such a manifold must have infinite volume.

scholarly journals On quotients of spaces with Ricci curvature bounded below

2018 ◽  
Vol 275 (6) ◽  
pp. 1368-1446 ◽  
Author(s):  
Fernando Galaz-García ◽  
Martin Kell ◽  
Andrea Mondino ◽  
Gerardo Sosa
Keyword(s):  
Ricci Curvature ◽  
Bounded Below

scholarly journals Almost Euclidean Isoperimetric Inequalities in Spaces Satisfying Local Ricci Curvature Lower Bounds

2018 ◽  
Vol 2020 (5) ◽  
pp. 1481-1510 ◽  
Author(s):  
Fabio Cavalletti ◽  
Andrea Mondino
Keyword(s):  
Riemannian Manifold ◽  
Isoperimetric Inequality ◽  
Ricci Curvature ◽  
Lower Bounds ◽  
Ricci Flow ◽  
General Framework ◽  
Isoperimetric Inequalities ◽  
Optimal Transportation ◽  
Maximal Volume ◽  
Bounded Below

Abstract Motivated by Perelman’s Pseudo-Locality Theorem for the Ricci flow, we prove that if a Riemannian manifold has Ricci curvature bounded below in a metric ball which moreover has almost maximal volume, then in a smaller ball (in a quantified sense) it holds an almost euclidean isoperimetric inequality. The result is actually established in the more general framework of non-smooth spaces satisfying local Ricci curvature lower bounds in a synthetic sense via optimal transportation.

scholarly journals On the structure of spaces with Ricci curvature bounded below. I

1997 ◽  
Vol 46 (3) ◽  
pp. 406-480 ◽  
Author(s):  
Jeff Cheeger ◽  
Tobias H. Colding
Keyword(s):  
Ricci Curvature ◽  
Bounded Below
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