Generic regularity of isoperimetric regions in dimension eight

2025/11/05 by Marshall-Stevens, Kobe, Niu, Gongping, Parise, Davide
#49Q10 #49Q20 #53A10 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2511.03795

Abstract

We establish generic regularity results for isoperimetric regions in closed Riemannian manifolds of dimension eight. In particular, we show that every isoperimetric region has a smooth nondegenerate boundary for a generic choice of smooth metric and enclosed volume, or for a fixed enclosed volume and a generic choice of smooth metric.

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