{"created":"2021-03-01T07:15:33.448153+00:00","id":53948,"links":{},"metadata":{"_buckets":{"deposit":"12c5cec4-80e1-43e4-881f-f61cce38fefd"},"_deposit":{"id":"53948","owners":[],"pid":{"revision_id":0,"type":"depid","value":"53948"},"status":"published"},"_oai":{"id":"oai:repository.dl.itc.u-tokyo.ac.jp:00053948","sets":["312:6865:8351:8352","9:504:6868:8353:8354"]},"item_4_biblio_info_7":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2019-03-22","bibliographicIssueDateType":"Issued"},"bibliographicIssueNumber":"1","bibliographicPageEnd":"139","bibliographicPageStart":"55","bibliographicVolumeNumber":"26","bibliographic_titles":[{"bibliographic_title":"Journal of Mathematical Sciences The University of Tokyo"}]}]},"item_4_description_5":{"attribute_name":"抄録","attribute_value_mlt":[{"subitem_description":"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. ","subitem_description_type":"Abstract"}]},"item_4_publisher_20":{"attribute_name":"出版者","attribute_value_mlt":[{"subitem_publisher":"Graduate School of Mathematical Sciences, The University of Tokyo"}]},"item_4_source_id_10":{"attribute_name":"書誌レコードID","attribute_value_mlt":[{"subitem_source_identifier":"AA11021653","subitem_source_identifier_type":"NCID"}]},"item_4_source_id_8":{"attribute_name":"ISSN","attribute_value_mlt":[{"subitem_source_identifier":"13405705","subitem_source_identifier_type":"ISSN"}]},"item_4_text_17":{"attribute_name":"Mathmatical Subject Classification","attribute_value_mlt":[{"subitem_text_value":"53C44(MSC2010)"},{"subitem_text_value":"58J35(MSC2010)"}]},"item_4_text_33":{"attribute_name":"原稿受領日","attribute_value_mlt":[{"subitem_text_value":"2018-03-01"}]},"item_4_text_4":{"attribute_name":"著者所属","attribute_value_mlt":[{"subitem_text_value":"School of Mathematical Sciences, Monash University"},{"subitem_text_value":"Centre for Geometric Analysis, Institute for Mathematics and its Applications, Faculty of Informatics and Engineering, University of Wollongong"}]},"item_creator":{"attribute_name":"著者","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"Bernard, Yann"}],"nameIdentifiers":[{"nameIdentifier":"160106","nameIdentifierScheme":"WEKO"}]},{"creatorNames":[{"creatorName":"Wheeler, Glen"}],"nameIdentifiers":[{"nameIdentifier":"160107","nameIdentifierScheme":"WEKO"}]},{"creatorNames":[{"creatorName":"Wheeler, Valentina-Mira"}],"nameIdentifiers":[{"nameIdentifier":"160108","nameIdentifierScheme":"WEKO"}]}]},"item_files":{"attribute_name":"ファイル情報","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2020-03-25"}],"displaytype":"detail","filename":"jms260103.pdf","filesize":[{"value":"464.6 kB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"jms260103.pdf","url":"https://repository.dl.itc.u-tokyo.ac.jp/record/53948/files/jms260103.pdf"},"version_id":"fa95660a-39cf-4360-a9a7-6b7f7d29f13d"}]},"item_keyword":{"attribute_name":"キーワード","attribute_value_mlt":[{"subitem_subject":"Curvature flow","subitem_subject_scheme":"Other"},{"subitem_subject":"global differential geometry","subitem_subject_scheme":"Other"},{"subitem_subject":"fourth order","subitem_subject_scheme":"Other"},{"subitem_subject":"geometric analysis","subitem_subject_scheme":"Other"},{"subitem_subject":"biharmonic","subitem_subject_scheme":"Other"},{"subitem_subject":"Chen conjecture","subitem_subject_scheme":"Other"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"eng"}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourcetype":"departmental bulletin paper","resourceuri":"http://purl.org/coar/resource_type/c_6501"}]},"item_title":"Concentration-Compactness and Finite-Time Singularities for Chen's Flow","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"Concentration-Compactness and Finite-Time Singularities for Chen's Flow"}]},"item_type_id":"4","owner":"1","path":["8352","8354"],"pubdate":{"attribute_name":"公開日","attribute_value":"2020-03-25"},"publish_date":"2020-03-25","publish_status":"0","recid":"53948","relation_version_is_last":true,"title":["Concentration-Compactness and Finite-Time Singularities for Chen's Flow"],"weko_creator_id":"1","weko_shared_id":null},"updated":"2022-12-19T04:31:19.974926+00:00"}