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arXiv · 2401.11962

A finiteness principle for distance functions on Riemannian surfaces with H\"older continuous curvature

Rotem Assouline
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Abstract

We study distance functions from geodesics to points on Riemannian surfaces with H\"older continuous Gauss curvature, and prove a finiteness principle in the spirit of Whitney extension theory for such functions. Our result can be viewed as a finiteness principle for isometric embedding of a certain type of metric spaces into Riemannian surfaces, with control over the H\"older seminorm of the Gauss curvature.

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Rotem Assouline. 2024-01-22. A finiteness principle for distance functions on Riemannian surfaces with H\"older continuous curvature. https://arxiv.org/abs/2401.11962

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