Open Access
July 2013 Isoperimetric and Weingarten surfaces in the Schwarzschild manifold
Simon Brendle, Michael Eichmair
J. Differential Geom. 94(3): 387-407 (July 2013). DOI: 10.4310/jdg/1370979333


We show that any star-shaped convex hypersurface with constant Weingarten curvature in the deSitter-Schwarzschild manifold 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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Simon Brendle. Michael Eichmair. "Isoperimetric and Weingarten surfaces in the Schwarzschild manifold." J. Differential Geom. 94 (3) 387 - 407, July 2013.


Published: July 2013
First available in Project Euclid: 11 June 2013

zbMATH: 1282.53053
MathSciNet: MR3080487
Digital Object Identifier: 10.4310/jdg/1370979333

Rights: Copyright © 2013 Lehigh University

Vol.94 • No. 3 • July 2013
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