| Co-Investigator(Kenkyū-buntansha) |
KOMORI Yohei Osaka City University, Faculty of Science, Assistant, 理学部, 助手 (70264794)
NISHIO Masaharu Osaka City University, Faculty of Science, Lecturer, 理学部, 講師 (90228156)
TANIGUCHI Masahiko Kyoto University, Garaduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (50108974)
KAMIYA Sigeyasu Okayama University of Science, Faculty of Technology, Professor, 工学部, 教授 (80122381)
NOGUCHI Junjiro Tokyo Institute of Technology, Faculty of Science, Professor, 理学部, 教授 (20033920)
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| Research Abstract |
The head investigator has been studying geometric and analytic objects on complex manifolds, especially on Riemann surfaces and Teichmuller spaces. In particular, using complex analysis, Kleinian groups, Teichmuller spaces, he studied Douady spaces of holomorphic maps between complex manifolds, estimates of numbers of holomorphic maps, relations between harmonic maps and holomorbhic maps, and so on. Let Hol (R,S) be the set of all non-constant holomorphic maps of a closed Riemann surface R of genus g to a closed Riemann surface S of genus g' with g', (2<less than or equal>g'<less than or equal>g'). Then an estimate of the number of elements in Hol (R,S) is obtained by topological data g and g'. Its method of proof is an area estimate by using hyperbolic geometry, Kleinian groups, and complex analysis. So this method is also applicable to the case of open Riemann surfaces of hyperbolic type. Harmonic maps between Riemann surfaces and holomorphic quadratic differentials are closely relat
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ed. From this point of view, relations between harmonic maps and holomorphic maps between Riemann surfaces are considered. It is proved that harmonic maps become holomorphic or anti-holomorphic under a certai
Komori studied semialgebraic description of Teichmuller space. Okumura obtained global real analytic angle parameters for Teichmuller spaces. Sakan considered non-quasiconformal harmonic extention. Taniguchi proved that Bloch topology of the universal Teichmuller space is equivalent to the geometric convergence in the sense of Caratheodory. Kamiya studied discrete subgroups of PSU (1,2, C)with Heisenberg translations. Masaoka obtained some important results on harmonic dimension of covering surfaces. Maitani considered ploblems on optimal embedding of Riemann surfaces.
Noguchi obtained the second main theorem of Cartan-Nevalinna theorem over function fields and its application to finiteness theorem for rational points. Toda obtained the fundamental inequality for non-degenerate holomorhic curves. Mori constructed some important examples for meromorphic maps of C^n into P^n (C) in the value distribution theorem. Nishio got a mean value property for polytemperatures. Less
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