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January 2017 Isoperimetric structure of asymptotically conical manifolds
Otis Chodosh, Michael Eichmair, Alexander Volkmann
J. Differential Geom. 105(1): 1-19 (January 2017). DOI: 10.4310/jdg/1483655857

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.

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Otis Chodosh. Michael Eichmair. Alexander Volkmann. "Isoperimetric structure of asymptotically conical manifolds." J. Differential Geom. 105 (1) 1 - 19, January 2017. https://doi.org/10.4310/jdg/1483655857

Information

Received: 17 April 2014; Published: January 2017
First available in Project Euclid: 5 January 2017

zbMATH: 1364.53035
MathSciNet: MR3592692
Digital Object Identifier: 10.4310/jdg/1483655857

Rights: Copyright © 2017 Lehigh University

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Vol.105 • No. 1 • January 2017
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