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Decomposition of the Möbius energy : the Möbius invariance and variational formulae of decomposed energies
https://doi.org/10.24561/00010398
https://doi.org/10.24561/00010398d9d445b4-12b4-4504-8740-e4a2d51ad2c9
名前 / ファイル | ライセンス | アクション |
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GD0000753.pdf (473.0 kB)
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Item type | 学位論文 / Thesis or Dissertation(1) | |||||||||
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公開日 | 2016-12-14 | |||||||||
タイトル | ||||||||||
言語 | en | |||||||||
タイトル | Decomposition of the Möbius energy : the Möbius invariance and variational formulae of decomposed energies | |||||||||
言語 | ||||||||||
言語 | eng | |||||||||
資源タイプ | ||||||||||
資源タイプ識別子 | http://purl.org/coar/resource_type/c_db06 | |||||||||
資源タイプ | doctoral thesis | |||||||||
ID登録 | ||||||||||
ID登録 | 10.24561/00010398 | |||||||||
ID登録タイプ | JaLC | |||||||||
アクセス権 | ||||||||||
アクセス権 | open access | |||||||||
アクセス権URI | http://purl.org/coar/access_right/c_abf2 | |||||||||
タイトル(別言語) | ||||||||||
その他のタイトル | 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 | |||||||||
著者 |
石関, 彩
× 石関, 彩
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著者 所属 | ||||||||||
埼玉大学大学院理工学研究科(博士後期課程)理工学専攻 | ||||||||||
著者 所属(別言語) | ||||||||||
Graduate School of Science and Engineering, Saitama University | ||||||||||
書誌 | ||||||||||
収録物名 | 博士論文(埼玉大学大学院理工学研究科(博士後期課程)) | |||||||||
書誌情報 |
発行日 2016 |
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出版者名 | ||||||||||
出版者 | 埼玉大学大学院理工学研究科 | |||||||||
出版者名(別言語) | ||||||||||
出版者 | Graduate School of Science and Engineering, Saitama University | |||||||||
形態 | ||||||||||
内容記述タイプ | Other | |||||||||
内容記述 | 89 p. | |||||||||
学位授与番号 | ||||||||||
学位授与番号 | 甲第1017号 | |||||||||
学位授与年月日 | ||||||||||
学位授与年月日 | 2016-03-24 | |||||||||
学位名 | ||||||||||
学位名 | 博士(理学) | |||||||||
学位授与機関 | ||||||||||
学位授与機関識別子Scheme | kakenhi | |||||||||
学位授与機関識別子 | 12401 | |||||||||
学位授与機関名 | 埼玉大学 | |||||||||
目次 | ||||||||||
内容記述タイプ | Other | |||||||||
内容記述 | Contents 1 Introduction 2 2 Known results 4 2.1 The existence of minimizers . . . . . . . . . . . . . . . . . . . . . 4 2.2 The Kusner-Sullivan conjecture . . . . . . . . . . . . . . . . . . . 5 2.3 The bi-Lipschitz continuity . . . . . . . . . . . . . . . . . . . . . 6 2.4 The regularity of critical points . . . . . . . . . . . . . . . . . . . 6 2.5 The gradient flow . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3 The decomposition theorem 8 4 The Möbius invariance 15 4.1 The invariance of the sum of energies . . . . . . . . . . . . . . . . 15 4.2 The invariance of each energy . . . . . . . . . . . . . . . . . . . . 20 4.3 Global minimizers of ε1 . . . . . . . . . . . . . . . . . . . . . . . 44 5 Variational formulae 44 5.1 The first variation . . . . . . . . . . . . . . . . . . . . . . . . . . 48 5.2 The second variation . . . . . . . . . . . . . . . . . . . . . . . . . 50 5.3 Estimates as multi-linear functional . . . . . . . . . . . . . . . . 53 5.4 L2-gradient expressions . . . . . . . . . . . . . . . . . . . . . . . 56 5.4.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . 57 5.4.2 The linear part . . . . . . . . . . . . . . . . . . . . . . . . 58 5.4.3 The nonlinear part . . . . . . . . . . . . . . . . . . . . . . 64 |
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注記 | ||||||||||
内容記述タイプ | Other | |||||||||
内容記述 | 主指導教員 : 長澤壯之 | |||||||||
版 | ||||||||||
[出版社版] | ||||||||||
著者版フラグ | ||||||||||
出版タイプ | VoR | |||||||||
出版タイプResource | http://purl.org/coar/version/c_970fb48d4fbd8a85 | |||||||||
資源タイプ | ||||||||||
内容記述タイプ | Other | |||||||||
内容記述 | text | |||||||||
フォーマット | ||||||||||
内容記述タイプ | Other | |||||||||
内容記述 | application/pdf | |||||||||
作成日 | ||||||||||
日付 | 2016-12-14 | |||||||||
日付タイプ | Created | |||||||||
アイテムID | ||||||||||
GD0000753 |