Generalized compactness for finite perimeter sets and applications to the isoperimetric problem
Abstract
For a complete noncompact connected Riemannian manifold with bounded geometry, we prove a 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 extends previous results contained in [Nar14a], in such a way that the generalized existence theorem, Theorem 1 of [Nar14a] is actually a generalized compactness theorem. The suitable modifications to the arguments and statements of the results in [Nar14a] are non-trivial. As a consequence we give a multipointed version of Theorem 1.1 of [LW11], and a simple proof of the continuity of the isoperimetric profile function.
Cite
@article{arxiv.1504.05104,
title = {Generalized compactness for finite perimeter sets and applications to the isoperimetric problem},
author = {Abraham Enrique Muñoz Flores and Stefano Nardulli},
journal= {arXiv preprint arXiv:1504.05104},
year = {2015}
}
Comments
Existence of isoperimetric region, isoperimetric profile, metric geometry. arXiv admin note: substantial text overlap with arXiv:1210.1328, arXiv:1503.02361