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Self-similar solutions to the hyperbolic mean curvature flow
Authors:Chunlei HE  Shoujun HUANG  Xiaomin XING
Institution:School of Mathematics and Computer Science, Anhui Normal University, Wuhu 241000, China
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.
Keywords:Hyperbolic mean curvature flow  self-similar solutions  35L10  35C06
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