Sharp Hölder continuity of tangent cones for spaces with a lower Ricci curvature bound and applications

2012/07/03 by Tobias Colding, Aaron Naber · 24 citations
Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Advanced Differential Geometry Research

paper · pdf · doi:10.4007/annals.2012.176.2.10

Abstract

We prove a new estimate on manifolds with a lower Ricci bound which asserts that the geometry of balls centered on a minimizing geodesic can change in at most a Hlder continuous way along the geodesic. We give examples that show that the Hlder exponent, along with essentially all the other consequences that follow from this estimate, are sharp.

Citations

• On the parabolic kernel of the Schrödinger operator
• Lower Bounds on Ricci Curvature and the Almost Rigidity of Warped Products

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