English

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

Classical Analysis and ODEs 2026-04-14 v1

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.

Keywords

Cite

@article{arxiv.2604.11418,
  title  = {A generalization of Reifenberg's theorem in R^N for flat cones},
  author = {Xiangyu Liang and Sicheng Zhang},
  journal= {arXiv preprint arXiv:2604.11418},
  year   = {2026}
}

Comments

55 pages, 4 figures