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http://dx.doi.org/10.4134/JKMS.2013.50.6.1311

CONTRACTION OF HOROSPHERE-CONVEX HYPERSURFACES BY POWERS OF THE MEAN CURVATURE IN THE HYPERBOLIC SPACE  

Guo, Shunzi (School of Mathematics and Computer Science Hubei University, School of Mathematics and Statistics Minnan Normal University)
Li, Guanghan (School of Mathematics and Computer Science Hubei University)
Wu, Chuanxi (School of Mathematics and Computer Science Hubei University)
Publication Information
Journal of the Korean Mathematical Society / v.50, no.6, 2013 , pp. 1311-1332 More about this Journal
Abstract
This paper concerns the evolution of a closed hypersurface of the hyperbolic space, convex by horospheres, in direction of its inner unit normal vector, where the speed equals a positive power ${\beta}$ of the positive mean curvature. It is shown that the flow exists on a finite maximal interval, convexity by horospheres is preserved and the hypersurfaces shrink down to a single point as the final time is approached.
Keywords
$H^{\beta}$-curvature flow; horosphere; convex hypersurface; hyperbolic space;
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