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DEFORMING PINCHED HYPERSURFACES OF THE HYPERBOLIC SPACE BY POWERS OF THE MEAN CURVATURE INTO SPHERES
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 Title & Authors
DEFORMING PINCHED HYPERSURFACES OF THE HYPERBOLIC SPACE BY POWERS OF THE MEAN CURVATURE INTO SPHERES
Guo, Shunzi; Li, Guanghan; Wu, Chuanxi;
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 Abstract
This paper concerns closed hypersurfaces of dimension in the hyperbolic space of constant sectional curvature evolving in direction of its normal vector, where the speed equals a power of the mean curvature. The main result is that if the initial closed, weakly h-convex hypersurface satisfies that the ratio of the biggest and smallest principal curvature at everywhere is close enough to 1, depending only on n and , then under the flow this is maintained, there exists a unique, smooth solution of the flow which converges to a single point in in a maximal finite time, and when rescaling appropriately, the evolving hypersurfaces exponential convergence to a unit geodesic sphere of .
 Keywords
powers of the mean curvature;horosphere;convex hypersurface;hyperbolic space;normalization;
 Language
English
 Cited by
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