1991 年度実績報告書

複素構造の解析学的・幾何学的研究

研究課題

研究課題/領域番号	03452008
研究機関	東京工業大学
研究代表者	野口潤次郎東京工業大学, 理学部, 教授 (20033920)
研究分担者	松崎克彦東京工業大学, 理学部, 助手 (80222298) 小島定吉東京工業大学, 理学部, 助教授 (90117705) 志賀啓成東京工業大学, 理学部, 助教授 (10154189) 西本敏彦東京工業大学, 理学部, 教授 (60016061) 吹田信之東京工業大学, 理学部, 教授 (90016022)
キーワード	複素構造 / 視素多様体 / リ-マン面 / モジュライ空間 / 正則写像 / 値分布 / 双曲空間 / クライン群
研究概要	上述の研究課題のもとでリ-マン面,複素多様体それでの間の正則写像、変形モジュライ空間の複素構造等々について解析的また幾何学的の両面から研究をして来た。研究成果広範かつ多岐に渡るが以下その主なものを述べる。その第1は1974年にS.Langにより予想された関数体上の双曲的空間に対ち了解の有限性が程完全に解決されたことである(野口)。これは色々な応用を含み,同時に予想されていたある写像空間の有限性も分る。これらは17年間未解決であった問題に解決を与えるものでその意義は大きい。他にも値分布,ア-ベル多様の族についての新らしい成果がある(野口)。リ-マン面間の正則写像の存在問題,ハ-ディ-空間とBMO関数空間に対する新しい知見も得られた(志賀啓)。3次元双曲空間で体積最小のものが明らかになったも著しい成果である(小島)。それらの空間の多面体分割の組合せ位相的性質も明らかにされた(小島)。クライン群の理論におけるエルゴ-ド性,ア-フォス予想に関する新らたな進展ももたらされた(松崎)。3階常微分方程式についてある場合にWKB法と呼ばれる解析が非常に役に立つことが分り新らしい事実が発見された(西本)。等角構造の研究は流体の解析に深く関連し,粘性流体の中を伝播する波に関するコ-シ-問題,初期値境界値問題が小さな初期値に対し大域的に解かれた(鵜飼)。その他確率論等からの成果も多々ある。また研究分担者を初め研究協力者も他研究機関の専門を同じくする研究者と研究交流,共同セミナ-が持たれ双方に有益な研究活動をすることが出来た。これらの研究活動で得られた知見による今後の研究の発展が期待出来る。

研究成果

(29件)

すべてその他

すべて文献書誌 (29件)

[文献書誌] T.Miyano: "Moduli spaces of harmonic and holomorphic mappings and Diophantine geometry" Lecture Notes in Mathematics. 1468. 227-253 (1991)
[文献書誌] J.Noguchi: "Moduli spaces of Abelian varieties with level structure over function fields" International Journal of Mathematics. 2. 183-194 (1991)
[文献書誌] J.Noguchi: "Hyperbolic Manifolds and Diophantine Geometry" Sugaku Exposition. 4. 63-81 (1991)
[文献書誌] J.Noguchi: "Moduli spaces of holomorphic mappings into hyperbolic spaces and its applications" Proc.Symp.Pure Math.,American Math.Soc.52. 397-401 (1991)
[文献書誌] J.Noguchi: "An example of a hyperbolic fiber space without hyperbolic embedding into compactification" to appear in Proc.Osaka International Conference,Osaka 1990.
[文献書誌] Y.Aihara: "Value distribution of meromorphic mappings into compactified locally symmetric spaces" Kodai Math.J.14. 320-334 (1991)
[文献書誌] M.Tanaka: "On misspecified linear model fittins" The Fourth ChinaーJapan Symp.on Statistics. 324-327 (1991)
[文献書誌] M.Tanaka: "Some properties of movingーaverage model fittings" to appear in J.Japan Statistical Soc.(1992)
[文献書誌] T.Shiga: "Some properties of solutions for oneーdimesional SPDEs associated with spaceーtime white noise" proc.3rd Nagoya Levy Seminar. 354-363 (1991)
[文献書誌] T.Shiga: "Ergodic theorems and exponetial decay of sample paths for interacting diffusion systems"
[文献書誌] H.Shiga: "Hardy spaces and BMO on Riemann surfaces" Lecture Notes in Math.1468. 84-93 (1991)
[文献書誌] S.Kojima: "Poyhedral decomposition of hyperbolic 3ーmanifolds with totally geodesic boundary" Adv.Study Pure Math.20.
[文献書誌] J.Noguchi: "Meromorphic mappings into compact hyperbolic complex spaces and geometric Diophantine problems" International J.Math.3. (1992)
[文献書誌] A.Inoue: "On a construction of a weak solution of the Hopf equation"
[文献書誌] M.Nakano: "On the WKB method for certain third order ordinary differential equations" Kodai Math.J.14. 432-462 (1991)
[文献書誌] C.BARDOS: "The classical incompressible NavierーStokes limit of the Boltzmann eqation" Math.Models Appl.Sci.1. 235-257 (1991)
[文献書誌] K.Mizohata: "The global existence of small amplitude solutions to the nonlinear acoustic eqaution" Research Rep.Info.Sci.,T.I.T. Aー106. (1991)
[文献書誌] S.Ukai: "Stationary solutions of the BGK model equation on a finite inteval with large boundary data" Research ReP.Info.Sci.,T.I.T.Aー107. (1991)
[文献書誌] S.Kojima: "The smallest hyperbolic 3ーmanifolds with totally geodesic boundary" J.Diff.Geom.34. 175-192 (1991)
[文献書誌] S.Kojima: "Shapes of stars" Proc.Amer.Math.Soc.
[文献書誌] S.Kojima: "Apollonian packings and hyperbolic geometry" to appear in Geometriae Dedicata.
[文献書誌] Y.Suzuki: "Hydrodynamic limit for a(0,10)ーvalued spin system"
[文献書誌] K.Matsuzaki: "Ergodic properties of discrete groups:inheritance to normal subgroups and invariance under quasiconformal deformations" J.Math.Kyoto Univ.
[文献書誌] K.Matsuzaki: "Geometric finiteness,quasiconformal stability and surjectivity of the Bers map for Kleinian groups" Tohoku Math.J.43. 327-336 (1991)
[文献書誌] K.Matsuzaki: "A characterization of extended schottky type groups with a remark to Ahlfors' conjecture" J.Math.Kyoto Univ.31. 358-367 (1991)
[文献書誌] J.Velling: "The action at infinity of conservative groups of hyperbolic motions need not have atoms" Ergodic Theory and Dynamical Systems. 11. 577-582 (1991)
[文献書誌] R.Kashima: "The word problem for free BCIーalgebras is decidable" Math.Jponica.
[文献書誌] T.Makino: "The global weak solutions of the compressible Euler equation with spherical symmetry"
[文献書誌] 高橋正子: "計算論ー計算可能性とラムダ計算ー" 近代科学社, 200 (1992)

1991 年度 実績報告書

複素構造の解析学的・幾何学的研究

研究代表者

野口 潤次郎 東京工業大学, 理学部, 教授 (20033920)

研究成果

[文献書誌] T.Miyano: "Moduli spaces of harmonic and holomorphic mappings and Diophantine geometry" Lecture Notes in Mathematics. 1468. 227-253 (1991)

[文献書誌] J.Noguchi: "Moduli spaces of Abelian varieties with level structure over function fields" International Journal of Mathematics. 2. 183-194 (1991)

[文献書誌] J.Noguchi: "Hyperbolic Manifolds and Diophantine Geometry" Sugaku Exposition. 4. 63-81 (1991)

[文献書誌] J.Noguchi: "Moduli spaces of holomorphic mappings into hyperbolic spaces and its applications" Proc.Symp.Pure Math.,American Math.Soc.52. 397-401 (1991)

[文献書誌] J.Noguchi: "An example of a hyperbolic fiber space without hyperbolic embedding into compactification" to appear in Proc.Osaka International Conference,Osaka 1990.

[文献書誌] Y.Aihara: "Value distribution of meromorphic mappings into compactified locally symmetric spaces" Kodai Math.J.14. 320-334 (1991)

[文献書誌] M.Tanaka: "On misspecified linear model fittins" The Fourth ChinaーJapan Symp.on Statistics. 324-327 (1991)

[文献書誌] M.Tanaka: "Some properties of movingーaverage model fittings" to appear in J.Japan Statistical Soc.(1992)

[文献書誌] T.Shiga: "Some properties of solutions for oneーdimesional SPDEs associated with spaceーtime white noise" proc.3rd Nagoya Levy Seminar. 354-363 (1991)

[文献書誌] T.Shiga: "Ergodic theorems and exponetial decay of sample paths for interacting diffusion systems"

[文献書誌] H.Shiga: "Hardy spaces and BMO on Riemann surfaces" Lecture Notes in Math.1468. 84-93 (1991)

[文献書誌] S.Kojima: "Poyhedral decomposition of hyperbolic 3ーmanifolds with totally geodesic boundary" Adv.Study Pure Math.20.

[文献書誌] J.Noguchi: "Meromorphic mappings into compact hyperbolic complex spaces and geometric Diophantine problems" International J.Math.3. (1992)

[文献書誌] A.Inoue: "On a construction of a weak solution of the Hopf equation"

[文献書誌] M.Nakano: "On the WKB method for certain third order ordinary differential equations" Kodai Math.J.14. 432-462 (1991)

[文献書誌] C.BARDOS: "The classical incompressible NavierーStokes limit of the Boltzmann eqation" Math.Models Appl.Sci.1. 235-257 (1991)

[文献書誌] K.Mizohata: "The global existence of small amplitude solutions to the nonlinear acoustic eqaution" Research Rep.Info.Sci.,T.I.T. Aー106. (1991)

[文献書誌] S.Ukai: "Stationary solutions of the BGK model equation on a finite inteval with large boundary data" Research ReP.Info.Sci.,T.I.T.Aー107. (1991)

[文献書誌] S.Kojima: "The smallest hyperbolic 3ーmanifolds with totally geodesic boundary" J.Diff.Geom.34. 175-192 (1991)

[文献書誌] S.Kojima: "Shapes of stars" Proc.Amer.Math.Soc.

[文献書誌] S.Kojima: "Apollonian packings and hyperbolic geometry" to appear in Geometriae Dedicata.

[文献書誌] Y.Suzuki: "Hydrodynamic limit for a(0,10)ーvalued spin system"

[文献書誌] K.Matsuzaki: "Ergodic properties of discrete groups:inheritance to normal subgroups and invariance under quasiconformal deformations" J.Math.Kyoto Univ.

[文献書誌] K.Matsuzaki: "Geometric finiteness,quasiconformal stability and surjectivity of the Bers map for Kleinian groups" Tohoku Math.J.43. 327-336 (1991)

[文献書誌] K.Matsuzaki: "A characterization of extended schottky type groups with a remark to Ahlfors' conjecture" J.Math.Kyoto Univ.31. 358-367 (1991)

[文献書誌] J.Velling: "The action at infinity of conservative groups of hyperbolic motions need not have atoms" Ergodic Theory and Dynamical Systems. 11. 577-582 (1991)

[文献書誌] R.Kashima: "The word problem for free BCIーalgebras is decidable" Math.Jponica.

[文献書誌] T.Makino: "The global weak solutions of the compressible Euler equation with spherical symmetry"

[文献書誌] 高橋 正子: "計算論ー計算可能性とラムダ計算ー" 近代科学社, 200 (1992)

1991 年度実績報告書

野口潤次郎東京工業大学, 理学部, 教授 (20033920)

[文献書誌] 高橋正子: "計算論ー計算可能性とラムダ計算ー" 近代科学社, 200 (1992)