A generalization of Reifenberg's theorem in RN for flat cones

2026/07/01 by Xiangyu Liang, Xicheng Zhang, Sicheng Zhang
Computer Science · Mathematics · #Topological and Geometric Data Analysis #Geometric and Algebraic Topology #Geometric Analysis and Curvature Flows

paper · doi:10.1112/jlms.70636

Abstract

Abstract In this paper, we prove that if a closed set in is close to a cone over a simplicial complex at each point and at each scale, then it is locally bi‐ 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.

Citations

• Solution of the Plateau problem for m-dimensional surfaces of varying topological type

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