Isoperimetric structure of asymptotically conical manifolds

Abstract

We study the isoperimetric structure of Riemannian manifolds that are asymptotic to cones with non-negative Ricci curvature. Specifically, we generalize to this setting the seminal results of G. Huisken and S.-T. Yau on the existence of a canonical foliation by volume preserving stable constant mean curvature surfaces at infinity of asymptotically flat manifolds as well as the results of the second-named author with S. Brendle and J. Metzger on the isoperimetric structure of asymptotically flat manifolds. We also include an observation on the isoperimetric cone angle of such manifolds. This result is a natural analogue of the positive mass theorem in this setting.

Cited by in corpus (7)

• Asymptotic isoperimetry on non collapsed spaces with lower Ricci bounds
• 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
• Asymptotically flat three-manifolds contain minimal planes
• Noncollapsed degeneration of Einstein 4-manifolds I
• Isoperimetric problem and structure at infinity on Alexandrov spaces with nonnegative curvature
• Curvature at the infinity of asymptotically flat Einstein manifold