2011 Fiscal Year Final Research Report
Conformal geometry of curves and surfaces and geometric knot theory
| Project/Area Number |
21540089
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Tokyo Metropolitan University |
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Principal Investigator |
IMAI Jun 首都大学東京, 大学院・理工学研究科・数理情報科学専攻, 准教授 (70221132)
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| Co-Investigator(Kenkyū-buntansha) |
KAMISHIMA Yoshinobu 首都大学東京, 大学院・理工学研究科, 教授 (10125304)
GUEST Martin 首都大学東京, 大学院・理工学研究科, 教授 (10295470)
SOMA Teruhiko 首都大学東京, 大学院・理工学研究科, 教授 (50154688)
AKAHO Manabu 首都大学東京, 大学院・理工学研究科, 助教 (30332935)
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| Research Collaborator |
LANGEVIN Remi ブルゴーニュ大学, ブルゴーニュ数学研究所, 教授
SOLANES Gil バルセロナ大学, 講師
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| Project Period (FY) |
2009 – 2011
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| Keywords | 微分トポロジー / 結び目のエネルギー |
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| Research Abstract |
A one-parameter family of renormalized potentials of a compact domain of an Euclidean space is introduced. A couple of sufficient conditions for the uniqueness of a point that gives the maximum(or minimum) value of the potential are given. The renormalization of the average of the squares of the linking numbers of a given knot and random circles, which can be considered as generalization of the renormalization of the integration of a potential on the domain, is studied. It turns out to be invariant under Mobius transformations.
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