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The L2-representations of the Second Variations and the Łojasiewicz Inequalities for Decomposed Möbius Energies
https://doi.org/10.24561/00018883
https://doi.org/10.24561/00018883692ac485-65ef-45bf-af3f-46660983f132
名前 / ファイル | ライセンス | アクション |
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GD0001096.pdf (334.0 kB)
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Item type | 学位論文 / Thesis or Dissertation(1) | |||||||||
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公開日 | 2020-03-02 | |||||||||
タイトル | ||||||||||
言語 | en | |||||||||
タイトル | The L2-representations of the Second Variations and the Łojasiewicz Inequalities for Decomposed Möbius Energies | |||||||||
言語 | ||||||||||
言語 | eng | |||||||||
キーワード | ||||||||||
主題Scheme | Other | |||||||||
主題 | the Möbius energy | |||||||||
キーワード | ||||||||||
主題Scheme | Other | |||||||||
主題 | decomposed Möbius energies | |||||||||
キーワード | ||||||||||
主題Scheme | Other | |||||||||
主題 | the second variation | |||||||||
キーワード | ||||||||||
主題Scheme | Other | |||||||||
主題 | the Łojasiewicz inequality | |||||||||
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 | 10.24561/00018883 | |||||||||
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 | 分解されたMöbiusエネルギーに対する第二変分のL2表現とŁojasiewicz不等式 | |||||||||
著者 |
郡司, 克徳
× 郡司, 克徳
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著者 ローマ字 | ||||||||||
GUNJI, Katsunori | ||||||||||
著者 所属 | ||||||||||
埼玉大学大学院理工学研究科(博士後期課程)理工学専攻数理電子情報コース | ||||||||||
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 2019 |
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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 | 62 p. | |||||||||
学位授与番号 | ||||||||||
学位授与番号 | 甲第1125号 | |||||||||
学位授与年月日 | ||||||||||
学位授与年月日 | 2019-03-20 | |||||||||
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 | |||||||||
抄録 | ||||||||||
内容記述タイプ | Abstract | |||||||||
内容記述 | Knot energies, one of which is the Möbius energy, are constructed to measure the well-proportionedness of the knot. The best-proportioned knot in the given knot class may be determined by the gradient flow of the energy. Indeed, Blatt showed the global existence and convergence of the gradient flow of the Möbius energy near stationary points. The Łojasiewicz inequality played an important role in proving the results. The inequality can be proved by properties of L2-representation of the first and second variations. On the other hand, Ishizeki and Nagasawa showed that the Möbius energy can be decomposed into parts keeping the Möbius invariance and each part has the L2-representation of the first variation. In this thesis, we discuss the L2-representation of the second variation for each decomposed part of the Mobius energy, and derive it explicitly. As a consequence of it and Chill's theory, the Łojasiewicz inequality is derived from the representations. | |||||||||
注記 | ||||||||||
内容記述タイプ | Other | |||||||||
内容記述 | 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 | 2020-03-02 | |||||||||
日付タイプ | Created | |||||||||
アイテムID | ||||||||||
GD0001096 |