Abraham Henrique Muñoz Flores - S. Nardulli
The isoperimetric problem of a complete Riemannian manifolds with a finite number of $C^0$-asymptotically Schwarzschild ends
Accepted Paper
Inserted: 11 mar 2015
Last Updated: 26 feb 2024
Journal: Comunications in Analysis and Geometry
Year: 2015
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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