A class of generalized fully nonlinear curvature flows and its applications

2022/06/04 by Jinrong Hu, Jiaqian Liu, Hu, Jinrong +5
Physics and Astronomy · Mathematics · #Advanced Differential Geometry Research #Geometric Analysis and Curvature Flows #Fixed Point Theorems Analysis

paper · pdf · doi:10.48550/arxiv.2206.01963

Abstract

In this paper, we concern a generalized fully nonlinear curvature flow involving k-th elementary symmetric function for principal curvature radii in Eulidean space \rnnn, k is an integer and 1≤ k≤ n-1. For 1≤ k< n-1, based on some initial data and constrains on smooth positive function defined on the unit sphere \sn, we obtain the long time existence and convergence of the flow. Especially, the same result shall be derived for k=n-1 without any constraint on the smooth positive function.

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