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http://dx.doi.org/10.4134/JKMS.j190637

A CLASS OF INVERSE CURVATURE FLOWS IN ℝn+1, II  

Hu, Jin-Hua (Faculty of Mathematics and Statistics Key Laboratory of Applied Mathematics of Hubei Province Hubei University)
Mao, Jing (Faculty of Mathematics and Statistics Key Laboratory of Applied Mathematics of Hubei Province Hubei University)
Tu, Qiang (Faculty of Mathematics and Statistics Key Laboratory of Applied Mathematics of Hubei Province Hubei University)
Wu, Di (Faculty of Mathematics and Statistics Key Laboratory of Applied Mathematics of Hubei Province Hubei University)
Publication Information
Journal of the Korean Mathematical Society / v.57, no.5, 2020 , pp. 1299-1322 More about this Journal
Abstract
We consider closed, star-shaped, admissible hypersurfaces in ℝn+1 expanding along the flow Ẋ = |X|α-1 F-β, α ≤ 1, β > 0, and prove that for the case α ≤ 1, β > 0, α + β ≤ 2, this evolution exists for all the time and the evolving hypersurfaces converge smoothly to a round sphere after rescaling. Besides, for the case α ≤ 1, α + β > 2, if furthermore the initial closed hypersurface is strictly convex, then the strict convexity is preserved during the evolution process and the flow blows up at finite time.
Keywords
Inverse curvature flows; star-shaped; principal curvatures;
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