2004 Fiscal Year Final Research Report Summary
Study of Discrete Subgroups of Rank 1 Simple Groups by Geometric Methods
| Project/Area Number |
13440019
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 | Nagoya University |
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Principal Investigator |
NAYATANI Shin Nagoya University, Graduate School of Mathematics, Associate Professor, 大学院・多元数理科学研究科, 助教授 (70222180)
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| Co-Investigator(Kenkyū-buntansha) |
EJIRI Norio Nagoya Institute of Technology, Shikumi domain, Professor, しくみ領域, 教授 (80145656)
KOBAYASHI Ryoichi Nagoya University, Graduate School of Mathematics, Professor, 大学院・多元数理科学研究科, 教授 (20162034)
OHTA Hiroshi Nagoya University, Graduate School of Mathematics, Associate Professor, 大学院・多元数理科学研究科, 助教授 (50223839)
IZEKI Hiroyasu Tokoku University, Graduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (90244409)
ITO Kentaro Nagoya University, Graduate School of Mathematics, Research Associate, 大学院・多元数理科学研究科, 助手 (00324400)
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| Project Period (FY) |
2001 – 2004
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| Keywords | fixed point theorem / quaternionic CR structure / minimal surface / lemma of logarithmic derivative / SL(2,C) representation space / crystal lattice / symplectic filling / deformation space of q.Fuchsian group |
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| Research Abstract |
Shin Nayatani and Hiroyasu Izeki studied combinatorial harmonic map theory and its application to super-rigidity and fixed point theorem, and proved fixed point theorems for isometric actions of discrete groups on CAT(O) spaces. Shin Nayatani and HIroyuku Kamada studied quaternionic CR geometry, and clarified the representation-theoretic meaning of the canonical pseudohermitian connection.
Norio Ejiri studied the existence problem for non-area-minimizing stable minimal surface of genus g in 2g-dimensional flat tori, and proved that there exists a non-holomorphic stable minimal surface of genus【greater than or equal】4 in a certain 8-dimensional torus.
Ryoichi Kobayashi srudied the construction of geometric theory of Diophantine approximation as discretization of the Nevanlinna theory, and showed that the lemma of logarithmic derivative for holomorphic curves in protective algebraic varieties hold always with the same form.
Toshihiro Nakanishi introduced a parameter complexifying R.C.Penner
… More
's λ length on the spaces of equivalence classes of faithful representations from surface groups into SL(2,C) mapping homotopy classes of boundary components to parabolic elements. Using this he succeeded in representing the mapping class groups as groups of rational transformations.
Motoko Kotani studied the large deviation of the random walk on a crystal lattice, that is, an infinite graph on which an abelian group acts and its geometric meaning. She determined asymptotic terms and clarified the relation between the rate function representing decay order and the tangent cone at infinity of a crystal lattice.
Hiroshi Ohta completely determined the deformation classes of symplectic fillings of the links of simple singularities and simple elliptic singularities. He also studied the obstruction and deformation theories of the Floer cohomology using filtered A_∞ algebras.
Takeshi Sato obtained some new algorithms to compute the value of π using various modular functions.
Hiroyuki Kamada studied compact complex surfaces admitting scalar flat Kahler metrics, and characterized the product of complex projective lines in terms of the existence of such metrics with a certain type of symmetry.
Kentaro Ito studied the boundary behavior of the deformation space of quasi-Fuchsian groups by means of the holonomy representations of projective structures on surfaces. He proved that Goldman's grafting theorem holds for the boundary groups by showing a certain kind of continuity and discreteness, thus resolving Bromberg's conjecture. Less
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