Journal of Differential Geometry

Isoperimetric and Weingarten surfaces in the Schwarzschild manifold

Simon Brendle and Michael Eichmair

Full-text: Open access

Abstract

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.

Article information

Source
J. Differential Geom. Volume 94, Number 3 (2013), 387-407.

Dates
First available in Project Euclid: 11 June 2013

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1370979333

Digital Object Identifier
doi:10.4310/jdg/1370979333

Mathematical Reviews number (MathSciNet)
MR3080487

Zentralblatt MATH identifier
1282.53053

Citation

Brendle, Simon; Eichmair, Michael. Isoperimetric and Weingarten surfaces in the Schwarzschild manifold. J. Differential Geom. 94 (2013), no. 3, 387--407. doi:10.4310/jdg/1370979333. https://projecteuclid.org/euclid.jdg/1370979333.


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