Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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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)
  • Received : 2012.12.28
  • Published : 2013.11.01
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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.

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References

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