Decomposition of the Möbius energy : the Möbius invariance and variational formulae of decomposed energies

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Decomposition of the Möbius energy : the Möbius invariance and variational formulae of decomposed energies

Persistent ID (NDL): info:ndljp/pid/10310733

Material type: 博士論文

Author: 石関, 彩

Publisher: 埼玉大学大学院理工学研究科

Publication date: 2016

Material Format: Digital

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Name of awarding university/degree: 埼玉大学,博士(理学)

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Note (General)：: type:textContents1 Introduction 22 Known results 42.1 The existence of minimizers . . . . . . . . . . . . . . . . . . . . . 42.2 The Kusner-Sullivan c...

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2023-09-05 再収集

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Material Type: 博士論文
Title: Decomposition of the Möbius energy : the Möbius invariance and variational formulae of decomposed energies
Author/Editor: 石関, 彩
Author Heading: 石関, 彩
Publication, Distribution, etc.: 埼玉大学大学院理工学研究科
Publication Date: 2016
Publication Date (W3CDTF): 2016
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
Periodical title: 博士論文（埼玉大学大学院理工学研究科（博士後期課程））
Degree grantor/type: 埼玉大学
Date Granted: 2016-03-24
Date Granted (W3CDTF): 2016-03-24
Dissertation Number: 甲第1017号
Degree Type: 博士(理学)
Conferring No. (Dissertation): 甲第1017号
Text Language Code: eng
Target Audience: 一般
Note (General): type:text
Contents1 Introduction 22 Known results 42.1 The existence of minimizers . . . . . . . . . . . . . . . . . . . . . 42.2 The Kusner-Sullivan conjecture . . . . . . . . . . . . . . . . . . . 52.3 The bi-Lipschitz continuity . . . . . . . . . . . . . . . . . . . . . 62.4 The regularity of critical points . . . . . . . . . . . . . . . . . . . 62.5 The gradient flow . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 The decomposition theorem 84 The Möbius invariance 154.1 The invariance of the sum of energies . . . . . . . . . . . . . . . . 154.2 The invariance of each energy . . . . . . . . . . . . . . . . . . . . 204.3 Global minimizers of ε1 . . . . . . . . . . . . . . . . . . . . . . . 445 Variational formulae 445.1 The first variation . . . . . . . . . . . . . . . . . . . . . . . . . . 485.2 The second variation . . . . . . . . . . . . . . . . . . . . . . . . . 505.3 Estimates as multi-linear functional . . . . . . . . . . . . . . . . 535.4 L2-gradient expressions . . . . . . . . . . . . . . . . . . . . . . . 565.4.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . 575.4.2 The linear part . . . . . . . . . . . . . . . . . . . . . . . . 585.4.3 The nonlinear part . . . . . . . . . . . . . . . . . . . . . . 64
主指導教員 : 長澤壯之
DOI: 10.24561/00010398
https://doi.org/10.24561/00010398
Persistent ID (NDL): info:ndljp/pid/10310733
https://dl.ndl.go.jp/pid/10310733
Collection: 障害者向け資料
Collection (Materials For Handicapped People:1): テキストデータ
Collection (particular): 国立国会図書館デジタルコレクション > デジタル化資料 > 博士論文
https://dl.ndl.go.jp/collections/A00014
Acquisition Basis: 博士論文（自動収集）
Date Accepted (W3CDTF): 2017-03-02T13:20:07+09:00
Date Created (W3CDTF): 2016-12-14
Format (IMT): application/pdf
Access Restrictions: 国立国会図書館内限定公開
Service for the Digitized Contents Transmission Service: 図書館・個人送信対象外
Availability of remote photoduplication service: 可
Periodical Title (URI): https://doi.org/10.24561/00010398
http://id.nii.ac.jp/1586/00010398/
Data Provider (Database): 国立国会図書館 : 国立国会図書館デジタルコレクション
https://dl.ndl.go.jp

Decomposition of the Möbius energy : the Möbius invariance and variational formulae of decomposed energies

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