A quantitative approach to the regularity of a Riemannian surface

2025/07/29 by Eilat, Matan
#Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2507.21921

Abstract

We introduce two definitions with the purpose of quantifying the concept of a C^2,α surface for 0 < α< 1. The intrinsic definition is given in terms of the α-Hölder norm of the Gauss curvature function. The extrinsic one relies on the existence of a smooth local representation of the Riemannian metric. We show that these definitions are equivalent up to a constant depending on α.

Citations

• The bi-Lipschitz constant of an isothermal coordinate chart
• Bounds on harmonic radius and limits of manifolds with bounded Bakry-Émery Ricci curvature

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