arXiv:1606.04626 Abstract | arXiv Analytics

arXiv:1606.04626 [math.DG]Abstract References Reviews Resources

Isoperimetric mass and isoperimetric regions in asymptotically flat manifold

Published 2016-06-15Version 1

In this paper, we study the isoperimetric mass of isoperimetric regions in asymptotically flat manifold $(M^3, g)$ with nonnegative scalar curvature and positive ADM mass. We prove that isoperimetric regions $\{\Omega_i\}$ with topological sphere boundary $\{\partial\Omega_i\}$ is an exhaustion of M. In addition, we reprove the result that isoperimetric mass equals the ADM mass in an elementary way.

Comments: 25 pages, no figures

Categories: math.DG

Subjects: 53C20, 83C99

Keywords: asymptotically flat manifold, isoperimetric regions, isoperimetric mass equals, positive adm mass, nonnegative scalar curvature

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