Isoperimetric structure of asymptotically conical manifolds
Differential Geometry
2019-07-01 v1
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.
Keywords
Cite
@article{arxiv.1503.05181,
title = {Isoperimetric structure of asymptotically conical manifolds},
author = {Otis Chodosh and Michael Eichmair and Alexander Volkmann},
journal= {arXiv preprint arXiv:1503.05181},
year = {2019}
}