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  Surfaces with maximal constant mean curvature

Metzger, J. (2013). Surfaces with maximal constant mean curvature. In Constant Mean Curvature Surfaces with Boundary. Springer Monographs in Mathematics, 13 (pp. 13-36).

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-5FF2-5 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-002C-5227-1
Genre: Book Chapter

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0712.3349v1.pdf (Preprint), 208KB
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 Creators:
Metzger, Jan1, Author              
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1Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, escidoc:24012              

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 Abstract: In this note we consider asymptotically flat manifolds with non-negative scalar curvature and an inner boundary which is an outermost minimal surface. We show that there exists an upper bound on the mean curvature of a constant mean curvature surface homologous to a subset of the interior boundary components. This bound allows us to find a maximizer for the constant mean curvature of a surface homologous to the inner boundary. With this maximizer at hand, we can construct an increasing family of sets with boundaries of increasing constant mean curvature. We interpret this familiy as a weak version of a CMC foliation.

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Language(s): eng - English
 Dates: 2013
 Publication Status: Published in print
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 Identifiers: eDoc: 328539
arXiv: 0712.3349
URI: http://lanl.arxiv.org/abs/0712.3349
DOI: 10.1007/978-3-642-39626-7_2
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Title: Constant Mean Curvature Surfaces with Boundary. Springer Monographs in Mathematics, 13
Source Genre: Book
 Creator(s):
López, R., Author
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Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 13 - 36 Identifier: -