Isoperimetric and weingarten surfaces in the schwarzschild manifold

Simon Brendle Stanford University Michael Eichmair ETH Z¨urich

Differential Geometry mathscidoc:1609.10319

Journal of Differential Geometry, 94, (3), 387-407, 2013
We show that any star-shaped convex hypersurface with constantWeingarten curvature in the deSitter-Schwarzschildmanifold is a sphere of symmetry.Moreover, we study an isoperimetric problem for bounded domains in the doubled Schwarzschild manifold. We prove the existence of an isoperimetric surface for any value of the enclosed volume, and we completely describe the isoperimetric surfaces for very large enclosed volume. This complements work in H. Bray’s thesis, where isoperimetric surfaces homologous to the horizon are studied.
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@inproceedings{simon2013isoperimetric,
  title={ISOPERIMETRIC AND WEINGARTEN SURFACES IN THE SCHWARZSCHILD MANIFOLD},
  author={Simon Brendle, and Michael Eichmair},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160914080712172862981},
  booktitle={Journal of Differential Geometry},
  volume={94},
  number={3},
  pages={387-407},
  year={2013},
}
Simon Brendle, and Michael Eichmair. ISOPERIMETRIC AND WEINGARTEN SURFACES IN THE SCHWARZSCHILD MANIFOLD. 2013. Vol. 94. In Journal of Differential Geometry. pp.387-407. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160914080712172862981.
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