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

2012/07/03 by Tobias Colding, Aaron Naber · 212 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Curvature #Geometric Analysis and Curvature Flows #Geometry #Geometry and complex manifolds #Mathematical analysis #Mathematics #Pure mathematics #Ricci curvature #Scalar curvature #Sectional curvature #Tangent #Upper and lower bounds

paper · pdf · doi:10.4007/annals.2012.176.2.10

published in Annals of Mathematics 176(2), 1173-1229 (Princeton University)

openalex publication_date 2012/07/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/27

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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