Inverse curvature flows in hyperbolic space

Details Inverse curvature flows in hyperbolic space Inverse curvature flows in hyperbolic space

2011-01-13

arxiv.org/abs/1101.2578v4

Journal Diff. Geom. 89, 487--527 (2011)

Mathematics

Differential Geometry

38 pages, v4: Dedication added; will appear in J. Diff. Geometry

Scientific paper

We consider inverse curvature flows in $\Hh$ with star-shaped initial
hypersurfaces and prove that the flows exist for all time, and that the leaves
converge to infinity, become strongly convex exponentially fast and also more
and more totally umbilic. After an appropriate rescaling the leaves converge in
$C^\infty$ to a sphere.

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