SELF-SIMILAR SOLUTIONS TO THE HYPERBOLIC MEAN CURVATURE FLOW  

作　　者：何春蕾 黄守军 邢晓敏 

机构地区：[1]School of Mathematics and Computer Science, Anhui Normal University, Wuhu 241000, China

出　　处：《Acta Mathematica Scientia》2017年第3期657-667,共11页数学物理学报（B辑英文版）

基　　金：supported in part by a grant from China Scholarship Council;the National Natural Science Foundation of China(11301006);the Anhui Provincial Natural Science Foundation(1408085MA01)

摘　　要：This article concerns the self-similar solutions to the hyperbolic mean curvature flow （HMCF） for plane curves, which is proposed by Kong, Liu, and Wang and relates to an earlier proposal for general flows by LeFloch and Smoczyk. We prove that all curves immersed in the plane which move in a self-similar manner under the HMCF are straight lines and circles. Moreover, it is found that a circle can either expand to a larger one and then converge to a point, or shrink directly and converge to a point, where the curvature approaches to infinity.This article concerns the self-similar solutions to the hyperbolic mean curvature flow （HMCF） for plane curves, which is proposed by Kong, Liu, and Wang and relates to an earlier proposal for general flows by LeFloch and Smoczyk. We prove that all curves immersed in the plane which move in a self-similar manner under the HMCF are straight lines and circles. Moreover, it is found that a circle can either expand to a larger one and then converge to a point, or shrink directly and converge to a point, where the curvature approaches to infinity.

关 键 词：Hyperbolic mean curvature flow self-similar solutions CURVATURE 

分 类 号：O186.1[理学—数学]