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Concentration-Compactness and Finite-Time Singularities for Chen's Flow
http://hdl.handle.net/2261/00079065
http://hdl.handle.net/2261/00079065340ec87f-b0ae-4575-a65f-3d449421f9bc
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
jms260103.pdf (464.6 kB)
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| Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||
|---|---|---|---|---|---|---|
| 公開日 | 2020-03-25 | |||||
| タイトル | ||||||
| タイトル | Concentration-Compactness and Finite-Time Singularities for Chen's Flow | |||||
| 言語 | ||||||
| 言語 | eng | |||||
| キーワード | ||||||
| 主題Scheme | Other | |||||
| 主題 | Curvature flow | |||||
| キーワード | ||||||
| 主題Scheme | Other | |||||
| 主題 | global differential geometry | |||||
| キーワード | ||||||
| 主題Scheme | Other | |||||
| 主題 | fourth order | |||||
| キーワード | ||||||
| 主題Scheme | Other | |||||
| 主題 | geometric analysis | |||||
| キーワード | ||||||
| 主題Scheme | Other | |||||
| 主題 | biharmonic | |||||
| キーワード | ||||||
| 主題Scheme | Other | |||||
| 主題 | Chen conjecture | |||||
| 資源タイプ | ||||||
| 資源 | http://purl.org/coar/resource_type/c_6501 | |||||
| タイプ | departmental bulletin paper | |||||
| 著者 |
Bernard, Yann
× Bernard, Yann× Wheeler, Glen× Wheeler, Valentina-Mira |
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| 著者所属 | ||||||
| 著者所属 | School of Mathematical Sciences, Monash University | |||||
| 著者所属 | ||||||
| 著者所属 | Centre for Geometric Analysis, Institute for Mathematics and its Applications, Faculty of Informatics and Engineering, University of Wollongong | |||||
| 抄録 | ||||||
| 内容記述タイプ | Abstract | |||||
| 内容記述 | Chen's flow is a fourth-order curvature flow motivated by the spectral decomposition of immersions, a program classically pushed by B.-Y. Chen since the 1970s. In curvature flow terms the flow sits at the critical level of scaling together with the most popular extrinsic fourth-order curvature flow, the Willmore and surface diffusion flows. Unlike them however the famous Chen conjecture indicates that there should be no stationary nonminimal data, and so in particular the flow should drive all closed submanifolds to singularities. We investigate this idea, proving that (1) closed data becomes extinct in finite time in all dimensions and for any codimension; (2) singularities are characterised by concentration of curvature in $L^n$ for intrinsic dimension $n \in \{2,4\}$ and any codimension (a Lifespan Theorem); and (3) for $n=2$ and in any codimension, there exists an explicit $\varepsilon_2$ such that if the $L^2$ norm of the tracefree curvature is initially smaller than $\varepsilon_2$, the flow remains smooth until it shrinks to a point, and that the blowup of that point is an embedded smooth round sphere. | |||||
| 書誌情報 |
Journal of Mathematical Sciences The University of Tokyo 巻 26, 号 1, p. 55-139, 発行日 2019-03-22 |
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| ISSN | ||||||
| 収録物識別子タイプ | ISSN | |||||
| 収録物識別子 | 13405705 | |||||
| 書誌レコードID | ||||||
| 収録物識別子タイプ | NCID | |||||
| 収録物識別子 | AA11021653 | |||||
| Mathmatical Subject Classification | ||||||
| 53C44(MSC2010) | ||||||
| Mathmatical Subject Classification | ||||||
| 58J35(MSC2010) | ||||||
| 出版者 | ||||||
| 出版者 | Graduate School of Mathematical Sciences, The University of Tokyo | |||||
| 原稿受領日 | ||||||
| 2018-03-01 | ||||||
