Isoperimetric structure of asymptotically conical manifolds

Otis Chodosh, Michael Eichmair, Alexander Volkmann

Research output: Contribution to journalArticle

2 Scopus citations

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 languageEnglish (US)
Pages (from-to)1-19
Number of pages19
JournalJournal of Differential Geometry
Volume105
Issue number1
DOIs
StatePublished - Jan 2017

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

Fingerprint Dive into the research topics of 'Isoperimetric structure of asymptotically conical manifolds'. Together they form a unique fingerprint.

  • Cite this