@phdthesis{oai:sucra.repo.nii.ac.jp:00010404,
 author = {石関, 彩},
 month = {},
 note = {89 p., 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, 主指導教員 : 長澤壯之, text, application/pdf},
 school = {埼玉大学},
 title = {Decomposition of the Möbius energy : the Möbius invariance and variational formulae of decomposed energies},
 year = {2016},
 yomi = {イシゼキ, アヤ}
}