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arXiv · 2604.11418

A generalization of Reifenberg's theorem in R^N for flat cones

Xiangyu Liang·Sicheng Zhang
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Abstract

In this paper we prove that if a closed set in R^N is close to a cone over a simplicial complex at each point and at each scale, then it is locally bi-H\"older equivalent to such a cone. This generalizes Reifenberg's Topological Disk Theorem in 1960 and G. David, T. De Pauw and T. Toro's result in 2008.

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Xiangyu Liang, Sicheng Zhang. 2026-04-13. A generalization of Reifenberg's theorem in R^N for flat cones. https://arxiv.org/abs/2604.11418

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