Journal of Differential Geometry

Isoperimetric structure of asymptotically conical manifolds

Otis Chodosh, Michael Eichmair, and Alexander Volkmann

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

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

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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.

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