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  1. 121 数理科学研究科
  2. Journal of Mathematical Sciences, the University of Tokyo
  3. 26
  4. 1
  1. 0 資料タイプ別
  2. 30 紀要・部局刊行物
  3. Journal of Mathematical Sciences, the University of Tokyo
  4. 26
  5. 1

Concentration-Compactness and Finite-Time Singularities for Chen's Flow

http://hdl.handle.net/2261/00079065
http://hdl.handle.net/2261/00079065
340ec87f-b0ae-4575-a65f-3d449421f9bc
名前 / ファイル ライセンス アクション
jms260103.pdf jms260103.pdf (464.6 kB)
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

WEKO 160106

Bernard, Yann

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Wheeler, Glen

× Wheeler, Glen

WEKO 160107

Wheeler, Glen

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Wheeler, Valentina-Mira

× Wheeler, Valentina-Mira

WEKO 160108

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
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
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