Regularity of sets of least perimeter in Riemannian manifolds

2023/06/16 by Aidan Backus, Backus, Aidan
Engineering · Mathematics · #3D Shape Modeling and Analysis #49Q05 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2306.09603

openalex publication_date 2023/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a short proof, in the tradition of the classical work of de Giorgi and Miranda on flat space, that the reduced boundary of a set of least perimeter in a Riemannian manifold of dimension ≤ 7 is a smooth minimal hypersurfaces.

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