Calculus of Variations and Geometric Measure Theory

Abraham Henrique Muñoz Flores - S. Nardulli

The isoperimetric problem of a complete Riemannian manifolds with a finite number of $C^0$-asymptotically Schwarzschild ends

created by nardulli on 11 Mar 2015
modified on 26 Feb 2024

[BibTeX]

Accepted Paper

Inserted: 11 mar 2015
Last Updated: 26 feb 2024

Journal: Comunications in Analysis and Geometry
Year: 2015

ArXiv: 1503.02361 PDF

Abstract:

We study the problem of existence of isoperimetric regions for large volumes, in $C^0$-locally asymptotically Euclidean Riemannian manifolds with a finite number of $C^0$-asymptotically Schwarzschild ends. Then we give a geometric characterization of these isoperimetric regions, extending previous results contained in EM13b, EM13a, and BE13. Moreover strengthening a little bit the speed of convergence to the Schwarzschild metric we obtain existence of isoperimetric regions for all volumes for a class of manifolds that we named $C^0$-strongly asymptotic Schwarzschild, extending results of BE13. Such results are of interest in the field of mathematical general relativity.


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