ISSN:
1420-8997
Keywords:
Killing and Geodesic Graph
;
Mean Curvature
;
Large Hypersurfaces
;
Alexandrov Reflection Technique
;
53 A 10
;
53 C 42
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract We consider embedded compact hypersurfacesM in a halfspace of hyperbolic space with boundary∂M in the boundary geodesic hyperplaneP of the halfspace and with non-zero constant mean curvature. We prove the following. Let {M n } be a sequence of such hypersurfaces with∂M n contained in a disk of radiusr n centered at a pointσ ε P such thatr n → 0 and that eachM n is a large. H-hypersurface,H 〉 1. Then there exists a subsequence of {M n } converging to the sphere of mean curvatureH tangent toP atσ. In the case of smallH-hypersurfaces orH ≤ 1, if we add a condition on the curvature of the boundary, there exists a subsequence of {M n } which are graphs. The convergence is smooth on compact subset of ℍ3 σ.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01229218
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