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タイトル: | Volume-preserving mean curvature flow for tubes in rank one symmetric spaces of non-compact type (Regularity, singularity and long time behavior for partial differential equations with conservation law) |
著者: | Koike, Naoyuki |
キーワード: | 53C44 53C35 |
発行日: | Apr-2020 |
出版者: | Research Institute for Mathematical Sciences, Kyoto University |
誌名: | 数理解析研究所講究録別冊 |
巻: | B80 |
開始ページ: | 57 |
終了ページ: | 80 |
抄録: | First we investigate the evolutions of the radius function and its gradient along the volume-preserving mean curvature flow starting from a tube (of nonconstant radius) over a compactclosed domain of a reflec tive submanifold in a symmetric space under certain condition for the radius function. Next, we prove that the tubeness is preserved along the flow in the casewhere the ambient space is a rank one symmetric space of non-compact type, the reective submanifold is an invariant submanifold and the radius function of the initial tube is radial. Furthermore, in this case, we prove that the ow reaches to the invariant submanifold or it exists in infinite time and converges to another tube of constant mean curvature in the C ∞- topology in infinite time. |
記述: | "Regularity, singularity and long time behavior for partial differential equations with conservation law". June 6-8, 2016. edited by Keiichi Kato, Mishio Kawashita, Masashi Misawa and Takayoshi Ogawa. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed. |
著作権等: | © 2020 by the Research Institute for Mathematical Sciences, Kyoto University. All rights reserved. |
URI: | http://hdl.handle.net/2433/260659 |
出現コレクション: | B80 Regularity, singularity and long time behavior for partial differential equations with conservation law |
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