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 [23] 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 [6] and J. Metzger [14, 15] 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.
Original language | English (US) |
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Pages (from-to) | 1-19 |
Number of pages | 19 |
Journal | Journal of Differential Geometry |
Volume | 105 |
Issue number | 1 |
DOIs | |
State | Published - Jan 2017 |
All Science Journal Classification (ASJC) codes
- Analysis
- Algebra and Number Theory
- Geometry and Topology