Flow by powers of the Gauss curvature. (English) Zbl 1401.35159
The authors prove that convex hypersurfaces in \(\mathbb{R}^{n+1}\) contracting under the flow by any power \(\alpha>\frac{1}{n+2}\) of the Gauss curvature converge after rescaling to fixed volume to a limit which is a smooth uniformly self-similar contracting solution of the flow. Under additional central symmetry assumption on the initial body, they show that the limit is the round sphere for any \(\alpha\geq 1\).
Reviewer: Shu-Yu Hsu (Min-hsiung)
MSC:
| 35K55 | Nonlinear parabolic equations |
| 35B65 | Smoothness and regularity of solutions to PDEs |
| 53A05 | Surfaces in Euclidean and related spaces |
Keywords:
entropy; Gauss curvature; monotonicity; regularity estimates; curvature image; entropy stability estimatesReferences:
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