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Foliations of Hyperbolic Space by Constant Mean Curvature Hypersurfaces.

Authors :
Coskunuzer, Baris
Source :
IMRN: International Mathematics Research Notices. Apr2010, Vol. 2010 Issue 8, p1417-1431. 15p. 1 Diagram.
Publication Year :
2010

Abstract

We show that the constant mean curvature hypersurfaces in Hn+1 spanning the boundary of a star-shaped C1,1 domain in S∞n(Hn+1) give a foliation of Hn+1. We also show that if Γ is a closed codimension-1 C2,α submanifold in S∞n(Hn+1) bounding a unique constant mean curvature hypersurface ΣH in Hn+1 with ∂∞ΣH = Γ for any H ∈ (−1,1), then the constant mean curvature hypersurfaces {ΣH} foliate Hn+1. [ABSTRACT FROM PUBLISHER]

Details

Language :
English
ISSN :
10737928
Volume :
2010
Issue :
8
Database :
Academic Search Index
Journal :
IMRN: International Mathematics Research Notices
Publication Type :
Academic Journal
Accession number :
49122112
Full Text :
https://doi.org/10.1093/imrn/rnp175