Self-similar Expanding Solutions for a Multiphase Mean Curvature Flow

• Main Authors: Wei-Hung Liao, 廖偉宏
• Other Authors: Ai-Nung Wang
• Format: Others
• Language: en_US
• Published: 2019
• Online Access: http://ndltd.ncl.edu.tw/handle/77352v

博士 === 國立臺灣大學 === 數學研究所 === 107 === We consider a multiphase surface C0 in R3 consisting of a finite number of surfaces passing through the origin , where all 1-dimensional junctions are regular triple junctions in which three planes meet at the same angle and each surface scales down homothetically to a limit curve of finite length. We prove the existence of self-similar expanding solutions of the mean curvature flow on the multiphase surface initially given by C0. For this initial C0, there are multiple solutions that are combinations of the regular triple junctions and regular quadruple points, where four regular triple junctions meet at an angle of approximately 109.5◦.