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arXiv · 1503.02361

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

Abraham Henrique Muñoz Flores·Stefano Nardulli
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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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Abraham Henrique Muñoz Flores, Stefano Nardulli. 2015-03-09. The isoperimetric problem of a complete Riemannian manifolds with a finite number of $C^0$-asymptotically Schwarzschild ends. https://doi.org/10.4310/cag.2020.v28.n7.a3

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