Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8900061 | Journal of Mathematical Analysis and Applications | 2018 | 45 Pages |
Abstract
This paper concerns closed, h-convex hypersurfaces of dimension nâ¥2 in the hyperbolic space Hκn+1 of constant sectional curvature κ evolving in direction of its normal vector, where the speed equals a power β>1 of a curvature function F, which is monotone, symmetric, homogeneous of degree 1. It is shown that if the initial h-convex hypersurface is pinched, then this is maintained under the flow, and the hypersurfaces shrink to a round point in Hκn+1 in finite time. As a consequence, when rescaling appropriately, the evolving hypersurfaces converge smoothly and exponentially to the unit sphere of Rn+1.
Keywords
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Physical Sciences and Engineering
Mathematics
Analysis
Authors
Guanghan Li, Yusha Lv,