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

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.

Revised version, 23 pages, 6 figures

References in corpus (1)

• Continuity and differentiability properties of the isoperimetric profile in complete noncompact Riemannian manifolds with bounded geometry

Cited by in corpus (4)

• On the existence of isoperimetric regions in manifolds with nonnegative Ricci curvature and Euclidean volume growth
• The isoperimetric problem via direct method in noncompact metric measure spaces with lower Ricci bounds
• Continuity and differentiability properties of the isoperimetric profile in complete noncompact Riemannian manifolds with bounded geometry
• A non-existence result for minimal catenoids in asymptotically flat spaces