A class of curvature flows expanded by support function and curvature function

Shanwei Ding; Guanghan Li

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arXiv · 2003.08570

A class of curvature flows expanded by support function and curvature function

Shanwei Ding·Guanghan Li

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Abstract

In this paper, we consider an expanding flow of closed, smooth, uniformly convex hypersurface in Euclidean \mathbb{R}^{n+1} with speed u^αf^β(α, β\in\mathbb{R}^1), where u is support function of the hypersurface, f is a smooth, symmetric, homogenous of degree one, positive function of the principal curvature radii of the hypersurface. If α\leq 0<β\leq 1-α, we prove that the flow has a unique smooth and uniformly convex solution for all time, and converges smoothly after normalization, to a round sphere centered at the origin.

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Shanwei Ding, Guanghan Li. 2020-03-19. A class of curvature flows expanded by support function and curvature function. https://arxiv.org/abs/2003.08570

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