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

Title & Authors
CONTRACTION OF HOROSPHERE-CONVEX HYPERSURFACES BY POWERS OF THE MEAN CURVATURE IN THE HYPERBOLIC SPACE
Guo, Shunzi; Li, Guanghan; Wu, Chuanxi;

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 $\small{{\beta}}$ 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
$\small{H^{\beta}}$-curvature flow;horosphere;convex hypersurface;hyperbolic space;
Language
English
Cited by
1.
DEFORMING PINCHED HYPERSURFACES OF THE HYPERBOLIC SPACE BY POWERS OF THE MEAN CURVATURE INTO SPHERES, Journal of the Korean Mathematical Society, 2016, 53, 4, 737
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