Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8904529 | Acta Mathematica Scientia | 2017 | 11 Pages |
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.
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Chunlei HE, Shoujun HUANG, Xiaomin XING,