SELF-SIMILAR SOLUTIONS TO THE HYPERBOLIC MEAN CURVATURE FLOW

doi:10.1016/S0252-9602(17)30028-0

数学物理学报(英文版) ›› 2017, Vol. 37 ›› Issue (3): 657-667.doi: 10.1016/S0252-9602(17)30028-0

SELF-SIMILAR SOLUTIONS TO THE HYPERBOLIC MEAN CURVATURE FLOW

何春蕾, 黄守军, 邢晓敏

School of Mathematics and Computer Science, Anhui Normal University, Wuhu 241000, China

收稿日期:2015-07-22 修回日期:2016-10-24 出版日期:2017-06-25 发布日期:2017-06-25
作者简介:Chunlei HE,E-mail:hcl026@126.com;Shoujun HUANG,sjhuang@mail.ahnu.edu.cn;Xiaomin XING,xmxing9204@126.com
基金资助:
This work was supported in part by a grant from China Scholarship Council,the National Natural Science Foundation of China (11301006),and the Anhui Provincial Natural Science Foundation (1408085MA01).

SELF-SIMILAR SOLUTIONS TO THE HYPERBOLIC MEAN CURVATURE FLOW

Chunlei HE, Shoujun HUANG, Xiaomin XING

School of Mathematics and Computer Science, Anhui Normal University, Wuhu 241000, China

Received:2015-07-22 Revised:2016-10-24 Online:2017-06-25 Published:2017-06-25
Supported by:
This work was supported in part by a grant from China Scholarship Council,the National Natural Science Foundation of China (11301006),and the Anhui Provincial Natural Science Foundation (1408085MA01).

摘要/Abstract

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.

关键词: Hyperbolic mean curvature flow, self-similar solutions, curvature

Abstract: 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.

Key words: Hyperbolic mean curvature flow, self-similar solutions, curvature

何春蕾, 黄守军, 邢晓敏. SELF-SIMILAR SOLUTIONS TO THE HYPERBOLIC MEAN CURVATURE FLOW[J]. 数学物理学报(英文版), 2017, 37(3): 657-667.

Chunlei HE, Shoujun HUANG, Xiaomin XING. SELF-SIMILAR SOLUTIONS TO THE HYPERBOLIC MEAN CURVATURE FLOW[J]. Acta mathematica scientia,Series B, 2017, 37(3): 657-667.

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SELF-SIMILAR SOLUTIONS TO THE HYPERBOLIC MEAN CURVATURE FLOW

SELF-SIMILAR SOLUTIONS TO THE HYPERBOLIC MEAN CURVATURE FLOW

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