Journal of Differential Geometry

Isoperimetric structure of asymptotically conical manifolds

Otis Chodosh, Michael Eichmair, and Alexander Volkmann

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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.

Article information

Source
J. Differential Geom., Volume 105, Number 1 (2017), 1-19.

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

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1483655857

Digital Object Identifier
doi:10.4310/jdg/1483655857

Mathematical Reviews number (MathSciNet)
MR3592692

Zentralblatt MATH identifier
1364.53035

Citation

Chodosh, Otis; Eichmair, Michael; Volkmann, Alexander. Isoperimetric structure of asymptotically conical manifolds. J. Differential Geom. 105 (2017), no. 1, 1--19. doi:10.4310/jdg/1483655857. https://projecteuclid.org/euclid.jdg/1483655857


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