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 [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)|
|Number of pages||19|
|Journal||Journal of Differential Geometry|
|State||Published - Jan 2017|
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Geometry and Topology