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Contraction of horosphere-convex hypersurfaces by powers of the mean curvature in the hyperbolic space

Chuanxi Wu|Guanghan Li|Shunzi Guo
대한수학회 (The Korean Mathematical Society)|2013.11|대한수학회지 (Journal of the KMS)|제50권 제6호|pp. 1311-1332

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참고문헌

키워드

hyperbolic spacehorosphereconvex hypersurfaceHβ-curvature flow
주제분류수학

초록

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 β 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.

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 β 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.

참고문헌 (26)

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