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

2015/04/20 by Abraham Enrique Muñoz Flores, Flores, Abraham Enrique Muñoz, Stefano Nardulli +1
Computer Science · Mathematics · #49Q05 #49Q20 #53A10 #58E99 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Geometric Analysis and Curvature Flows #Metric Geometry (math.MG) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1504.05104

openalex publication_date 2015/04/20 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

For a complete noncompact connected Riemannian manifold with bounded\ngeometry, we prove a compactness result for sequences of finite perimeter sets\nwith uniformly bounded volume and perimeter in a larger space obtained by\nadding limit manifolds at infinity. We extends previous results contained in\n[Nar14a], in such a way that the generalized existence theorem, Theorem 1 of\n[Nar14a] is actually a generalized compactness theorem. The suitable\nmodifications to the arguments and statements of the results in [Nar14a] are\nnon-trivial. As a consequence we give a multipointed version of Theorem 1.1 of\n[LW11], and a simple proof of the continuity of the isoperimetric profile\nfunction.\n

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