Regularity of sets of least perimeter in Riemannian manifolds

Author:

Aidan Backus

Keyword:

Mathematics, Differential Geometry, Differential Geometry (math.DG), Analysis of PDEs (math.AP)

journal:

date:

2023-06-15 16:00:00

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 $\leq 7$ is a smooth minimal hypersurfaces.

PDF: Regularity of sets of least perimeter in Riemannian manifolds.pdf