Calculus of Variations and Geometric Measure Theory

S. Nardulli - A. Enrique Muñoz Flores

Generalized compactness for finite perimeter sets and applications to the isoperimetric problem

created by nardulli on 15 Apr 2015
modified on 11 Jan 2022


Published Paper

Inserted: 15 apr 2015
Last Updated: 11 jan 2022

Journal: Journal of Dynamical and Control Systems
Volume: 28
Pages: 59–69
Year: 2022
Doi: 10.1007/s10883-020-09517-y
Links: Journal Link


For a complete noncompact Riemannian manifold with bounded geometry, we prove a “generalized” compactness result for sequences of finite perimeter sets with uniformly bounded volume and perimeter in a larger space obtained by adding limit manifolds at infinity. We extend previous results contained in Nardulli (Asian J Math 18(1):1–28, 2014), in such a way that the main theorem is a generalization of the generalized existence theorem, i.e., Theorem 1 of Nardulli (Asian J Math 18(1):1–28, 2014). We replace C2,α locally asymptotic bounded geometry with C0 locally asymptotic bounded geometry.

Tags: GeMeThNES