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A class of curvature flows expanded by support function and curvature function (2003.08570v1)
Published 19 Mar 2020 in math.DG
Abstract: In this paper, we consider an expanding flow of closed, smooth, uniformly convex hypersurface in Euclidean \mathbb{R}{n+1} with speed u\alpha f\beta (\alpha, \beta\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 \alpha \leq 0<\beta\leq 1-\alpha, 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.