{"created":"2023-05-15T15:23:32.708686+00:00","id":10404,"links":{},"metadata":{"_buckets":{"deposit":"c330f4c5-6e30-4c75-be43-81a8280e7cc3"},"_deposit":{"created_by":15,"id":"10404","owners":[15],"pid":{"revision_id":0,"type":"depid","value":"10404"},"status":"published"},"_oai":{"id":"oai:sucra.repo.nii.ac.jp:00010404","sets":["94:429:431:432:508"]},"author_link":[],"item_113_alternative_title_1":{"attribute_name":"タイトル（別言語）","attribute_value_mlt":[{"subitem_alternative_title":"メビウス・エネルギーの分解：分解されたエネルギーのメビウス不変性と変分公式"}]},"item_113_biblio_info_9":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2016","bibliographicIssueDateType":"Issued"}}]},"item_113_date_35":{"attribute_name":"作成日","attribute_value_mlt":[{"subitem_date_issued_datetime":"2016-12-14","subitem_date_issued_type":"Created"}]},"item_113_date_granted_20":{"attribute_name":"学位授与年月日","attribute_value_mlt":[{"subitem_dategranted":"2016-03-24"}]},"item_113_degree_grantor_22":{"attribute_name":"学位授与機関","attribute_value_mlt":[{"subitem_degreegrantor":[{"subitem_degreegrantor_name":"埼玉大学"}],"subitem_degreegrantor_identifier":[{"subitem_degreegrantor_identifier_name":"12401","subitem_degreegrantor_identifier_scheme":"kakenhi"}]}]},"item_113_degree_name_21":{"attribute_name":"学位名","attribute_value_mlt":[{"subitem_degreename":"博士(理学)"}]},"item_113_description_13":{"attribute_name":"形態","attribute_value_mlt":[{"subitem_description":"89 p.","subitem_description_type":"Other"}]},"item_113_description_24":{"attribute_name":"目次","attribute_value_mlt":[{"subitem_description":"Contents\n1 Introduction 2\n2 Known results 4\n2.1 The existence of minimizers . . . . . . . . . . . . . . . . . . . . . 4\n2.2 The Kusner-Sullivan conjecture . . . . . . . . . . . . . . . . . . . 5\n2.3 The bi-Lipschitz continuity . . . . . . . . . . . . . . . . . . . . . 6\n2.4 The regularity of critical points . . . . . . . . . . . . . . . . . . . 6\n2.5 The gradient flow . . . . . . . . . . . . . . . . . . . . . . . . . . . 7\n3 The decomposition theorem 8\n4 The Möbius invariance 15\n4.1 The invariance of the sum of energies . . . . . . . . . . . . . . . . 15\n4.2 The invariance of each energy . . . . . . . . . . . . . . . . . . . . 20\n4.3 Global minimizers of ε1 . . . . . . . . . . . . . . . . . . . . . . . 44\n5 Variational formulae 44\n5.1 The first variation . . . . . . . . . . . . . . . . . . . . . . . . . . 48\n5.2 The second variation . . . . . . . . . . . . . . . . . . . . . . . . . 50\n5.3 Estimates as multi-linear functional . . . . . . . . . . . . . . . . 53\n5.4 L2-gradient expressions . . . . . . . . . . . . . . . . . . . . . . . 56\n5.4.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . 57\n5.4.2 The linear part . . . . . . . . . . . . . . . . . . . . . . . . 58\n5.4.3 The nonlinear part . . . . . . . . . . . . . . . . . . . . . . 64","subitem_description_type":"Other"}]},"item_113_description_25":{"attribute_name":"注記","attribute_value_mlt":[{"subitem_description":"主指導教員 : 長澤壯之","subitem_description_type":"Other"}]},"item_113_description_33":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"subitem_description":"text","subitem_description_type":"Other"}]},"item_113_description_34":{"attribute_name":"フォーマット","attribute_value_mlt":[{"subitem_description":"application/pdf","subitem_description_type":"Other"}]},"item_113_dissertation_number_19":{"attribute_name":"学位授与番号","attribute_value_mlt":[{"subitem_dissertationnumber":"甲第1017号"}]},"item_113_identifier_registration":{"attribute_name":"ID登録","attribute_value_mlt":[{"subitem_identifier_reg_text":"10.24561/00010398","subitem_identifier_reg_type":"JaLC"}]},"item_113_publisher_11":{"attribute_name":"出版者名","attribute_value_mlt":[{"subitem_publisher":"埼玉大学大学院理工学研究科"}]},"item_113_publisher_12":{"attribute_name":"出版者名（別言語）","attribute_value_mlt":[{"subitem_publisher":"Graduate School of Science and Engineering, Saitama 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