The isoperimetric problem of a complete Riemannian manifold with a finite number of C⁰‑asymptotically Schwarzschild ends

We study the problem of existence of isoperimetric regions for large volumes, in C⁰-locally asymptotically Euclidean Riemannian manifolds with a finite number of C⁰-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 C⁰-strongly asymptotic Schwarzschild, extending results of [BE13]. Such results are of interest in the field of mathematical general relativity.