The isoperimetric inequality on asymptotically flat manifolds with nonnegative scalar curvature

Abstract

In this note, we consider the isoperimetric inequality on an asymptotically flat manifold with nonnegative scalar curvature, and improve it by using Hawking mass. We also obtain a rigidity result when equality holds for the classical isoperimetric inequality on an asymptotically flat manifold with nonnegative scalar curvature.

Final version, to appear International Mathematics Research Notices. 12 pages, no figures

Cited by in corpus (2)

• Large isoperimetric regions in asymptotically hyperbolic manifolds
• Rigidity of Hawking mass for surfaces in three manifolds