Communications in Analysis and Geometry
Volume 28 (2020)
The isoperimetric problem of a complete Riemannian manifold with a finite number of $C^0$‑asymptotically Schwarzschild ends
Pages: 1577 – 1601
We show existence and we give a geometric characterization of isoperimetric regions for large volumes, in $C^2$-locally asymptotically Euclidean Riemannian manifolds with a finite number of $C^0$-asymptotically Schwarzschild ends. This work extends 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.
The first-named author was partially supported by Capes.
Received 24 July 2016
Accepted 22 April 2018
Published 7 December 2020