Embedded CMC Hypersurfaces on Hyperbolic Spaces
In this paper we will prove that for every integer n>1, there exists a real number H0<-1 such that every H∈ (-∞,H0) can be realized as the mean curvature of an embedding of Hn-1\times S¹ in the n+1-dimensional space Hn+1. For n=2 we explicitly compute the value H0. For a general value n, we provide a function ξn defined on (-∞,-1), which is easy to compute numerically, such that, if ξn(H)>-2π, then, H can be realized as the mean curvature of an embedding of Hn-1\times S¹ in the (n+1)-dimensional space Hn+1.
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| Main Author: | |
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| Format: | Digital revista |
| Language: | English |
| Published: |
Universidad Nacional de Colombia y Sociedad Colombiana de Matemáticas
2011
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| Online Access: | http://www.scielo.org.co/scielo.php?script=sci_arttext&pid=S0034-74262011000100006 |
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