幾何学的複素解析

1997 Fiscal Year Annual Research Report

• Project/Area Number: 09304014
• Research Category: Grant-in-Aid for Scientific Research (A)
• Research Institution: Tokyo Institute of Technology
• Principal Investigator: 野口 潤次郎 東京工業大学, 理学部, 教授 (20033920)
• Co-Investigator(Kenkyū-buntansha): 満渕 俊樹 大阪大学, 大学院・理学研究科, 教授 (80116102) ; 大沢 健夫 名古屋大学, 大学院・多元数理科学研究科, 教授 (30115802) ; 藤本 坦考 金沢大学, 理学部, 教授 (60023595) ; 志賀 啓成 東京工業大学, 理学部, 助教授 (10154189) ; 辻 元 東京工業大学, 理学部, 助教授 (30172000)
• Keywords: 多変数複素解析 / 幾何学的複素解析 / 小林双曲的多様体 / 値分布 / 不変計量 / モジュライ理論 / 擬凸領域 / タイヒミューラー理論

Research Abstract

高次元値分布理論・複素双曲的多様体について、野口潤次郎は初めて任意次元の双曲的射影超曲面の存在を示し、更にその関数体上の有理点集合及び代数体の単元点集合の有限性を証明した。藤本坦考は、N次元射影空間への線形的非退化有理型写像で、3N+1個の一般の位置にある超平面の逆像が重複度2まで等しければ高々2個であるという新しい形の一意性定理を得た。
擬凸領域の解析及び∂^^-方程式の理論を複素幾何へ応用する研究では、大沢健夫は次元2以上の複素射影空間内に可微分なLevi平坦超曲面が存在しないことを示し、弱擬凸領域上のBergman計量の法線方向の増大度を決定した。辻元は一般型の代数多様体の普遍被覆の商が再び一般型になることを保型形式を∂^^-評価を用いて構成することにより示した。また、豊富な直線束LにたいしてK_X+mLがm【greater than or equal】>n(n+1)/2のとき自由であること特異計量を用いてしめした。
複素多様体、CR多様体の研究については、満渕俊樹は、Calabi予想に関し、Fano多様体についての安定性とKahler-Einstein計量の存在についてのTianの最近の仕事のgapを埋める作業を、Lin Wengと行った。吉川謙一は、Quillen計量の退化問題を研究し、部分的な解決を与えた。児玉秋雄は、複素ユークリッド空間内の一般複素楕円体の、正則自己同型群からの特徴付けの問題を研究し、ある種の場合にはWebsterのCR不変計量を有効に用いることができることが分かった
リーマン面、タイヒミューラー理論と複素力学系の研究で、志賀啓成はフックス群の変形のある種の安定性,容量0の集合の擬等角不変性,リーマン面の正則族,複素力学系の正則族のRigidity等の結果を得た。多変数では、西村保一郎が複素2次元射影空間上の,2次多項式双有理写像を分類した。またいくつかの族の定める複素力学系の研究をした。

Research Products

• [Publications] J. Nogushi: "Recent topics in the theory of holomorphic curves." Proc.Internat.Workshop on the Value Distribution Theory and its Applications,July 1996,. 317-331 (1997)
• [Publications] J. Noguchi: "Nevanlinna-Cartan theory over function fields and a Diophantine equation," J. reine augew.Math. 487. 61-83 (1997)
• [Publications] K. Watanabe: "Cousin problems and holomorphic cocycles" Mathematica Japonica. 47・1. (1997)
• [Publications] K. Watanabe: "Weierstrass points of the Fermat curve" Proceedings of the Congress ISAAC'97,Univ.of Delaware. 1997.
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• [Publications] M.Kato Appell'sF4 with finite irreducible monodromy group: Kyushu J.of Math.51. 125-147 (1997)
• [Publications] 満渕俊樹: "アインシュタイン計量とモジュライ空間" 数理物理への誘い2(最新の動向をめぐって)(荒木不二洋編). 95-113 (1997)
• [Publications] Y. Yoshida 他3名共: "On the extension of holomorphic mappings of weak type" Fukuoka University Science Reports. 27-2. 55-63 (1997)
• [Publications] T. Akahori and K. Miyajima: "A smoothness of deformations of normal strongly pseudo-convex CR-structures" Kyushuu J Math.(1997)
• [Publications] T. Akahori: "Deformation theory of CR-structures and its application to deformations of isolated singularites I" Adv.Studies in Pure Math.25. 1-40 (1997)
• [Publications] S. Takeuchi: "On tensor products and dual spaces of CR vector spaces" Sci.Rep.Fac.Ed.Gifu Univ.岐阜大学教育学部研究報告自然科学. 22-1. 1-5 (1997)
• [Publications] S. Takeuchi: "Generalized Serre problem and the peudoconvexity of reductive complex Lie group actions on complex manifolds" Proc.5th Internat.Conf.Finite and Infinite Dimensional Complex Analysis Peking University,1997 August.
• [Publications] K.I. Yosikawa: "Degeneration of algebraic manifolds and the spectrum of Laplacian" Nagoya Math.J.146. :83-129 (:1997)
• [Publications] Y. Aihara: "Finiteness theorems for meromorphic mappings" Osaka J.Math. (1997)
• [Publications] J. Kamimoto: "Singularities of the Bergman kernel for certain weakly pseudoconvex domains" J.Math.Scie.University of Tokyo. (1997)
• [Publications] J. Kamimoto: "On an integral of Hardy and Littlewood" Kyushu J.Math.(1997)
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• [Publications] T. Jimbo and A. Sakai: "Polynominal hulls of graphs on the sphere" Proc.Fifth Internat.Conf.Complex Analysis,Peking University,.
• [Publications] Y. Abe: ":Universal holomorphic functions in several variables" Analysis. 17. 71-77 (1997)
• [Publications] K. Takegoshi: "On cohomology groups of nef line bundles tensorized with multiplier ideal sheaves on compact Kahler manifolds" Osaka J.Math.
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• [Publications] :K. Takegoshi: ":A volume estimate for strong subharmonicity and maximum principle on complete Riemannian manifolds" Nagoya Math.J.1997.
• [Publications] K. Takegoshi: "A maximum principle for P-harmonic maps with L^q finite energy" Proc.Amer.Math.Soc.
• [Publications] Y.Nishimura: "Another Green function for some birational maps of P^2" 数理解析研究所講究録. 988. 192-206 (1997)
• [Publications] K. Azukawa: "A role od Fibonacci numbers in sunflower patterns" Forma. 12. :35-37 (1997)
• [Publications] N. Levenberg and H. Yamaguchi: "Robin functions for complex manifolds and application" CR geometry と 特異点 数理解析研究所講究録. (1997)
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• [Publications] K. Adachi and H-R.Cho: "L^p(1【less than or equal】p【less than or equal】∞)estimates for ∂^n on a certain pseudoconvex domain in C^n" Nagoya Math.J.148. 1-10 (1997)
• [Publications] K. Adachi and H.-R.Cho: "H^p and L^p extensions of holomorphic functions from subvarieties to certain convex domains" Math.J.Toyama Univ.20. 1-13 (1997)
• [Publications] T. Umeno: "Complex Line Bundles on Toroidal Groups" Proc.First Congress of ISAAC,Kluwer Publishers. (1997)
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• [Publications] 宮嶋公夫: "強擬凸CR構造の変形と正規孤立特異点の変形" 数理解析研究所講究録.
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• [Publications] N. Toda: "On the fundamental inequality for non-degenerate holomorphic curves" Kodai math.J.29. 178-196 (1997)
• [Publications] N. Toda: "On the fine cluster set of holomorphic curves" Bull.Nagoya I.T.49. 123-130 (1997)
• [Publications] N. Toda: "On the number of asymptotic points of holomorphic curves" Proc.Japan Acad.73,Ser.A. 176-180 (1997)
• [Publications] K. Ishizaki and K. Tohge: "On the complex oscillation of some linear differential equations" J.Math.Anal.Appl.206. 503-517 (1997)
• [Publications] K. Isizaki: "An oscillation results for a certain linear differential equation of second order" Hokkaido J.Math.26. 421-434 (1997)
• [Publications] K. Ishizaki: "On the Schwarzian differential equation{w,z}=R(z,w)" Kodai Math.J.20. 67-78 (1997)
• [Publications] K. Ishizaki: "A result for a certain algebraic differential equation" Bull.Hong Kong Math.Soc.
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• [Publications] S. Saitoh: "Natural norm inequalities in nonlinear transforms" General Inequalities. 7. 39-52 (1997)
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• [Publications] S. Saitoh: "Linear integro-differential equations and their applications" Proc.Volterra Centennial Symp.
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• [Publications] G. Schmieder and M. Shiba: "Realisierungen des Idealen Randes einer Riemannschen Flache unter konformen Abschlie Bungen" Archiv der Mathematik. 68. 36-44 (1997)
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• [Publications] G. Schmieder and M. Shiba: "One-parameter variations of the ideal boundary and compact continuations of a Riemann surface" Analysis.
• [Publications] S. Tajima: "Grothendieck residue calculus and holonomic D-modules" Proc.5th Internat.Conf.on Finite or Infinite Complex Analysis,Beijing,1997.
• [Publications] S. Tajima: "Geometric Phases and Bloch Electrons" JSPS-DOST Lecture Notes in Mathematics. 5. 63 (1997)
• [Publications] S. Tajima: "Bloch function in an external electric field and Berry-Buslaev phase" New Trends in Microlocal Analysis(eds by J-M.Bony and M. Morimoto),Springer. 143-156 (1997)
• [Publications] S. Tajima: "Direct image of the de Rham system associated with a rational double point" Differential Geometry and Mathematical Physics Banach Center publ., Polish Acad,Warszawa. 39. 155-160 (1997)
• [Publications] M.Bonk, D.Minda and H.Yanagihara: "Distortion estimates for locally univalent Bloch functions" Pacific J.of Math.179-2. 241 (1997)
• [Publications] M.Bonk, D.Minda and H.Yanagihara: "Distortion estimates for Bloch functions" Journal d'Analyse Math.69. 73 (1996)
• [Publications] S.Yamashita: "Slender sets for an elliptic partial differential equation with applications" Math.Japonica. 45. 457-481 (1997)
• [Publications] S.Yamashita: "Poincare and the spherical densities" Mathematica Japonica. 46. 433-438 (1997)
• [Publications] S.Yamashita: "Goluzin's extension of the Schwarz-Pick inequalities" J.Inequalities and Applications. 1. 345-356 (1997)
• [Publications] S.Yamashita: "Special solutions of the Liouville equation" Mathematica Japonica.
• [Publications] 森下博,小林尚弘,高市英明,天野要,四ツ谷晶二: "代用電荷法によるポアソン方程式の数値計算" 情報処理学会論文誌. 38-8. 1483-1491 (1997)
• [Publications] K.Amano and M.Sugihara: "Numerical conformal mapping onto parallel slit domains with application to potential flow analysis" Theoretical and Applied Mechanics. 46. 295-305 (1997)
• [Publications] K.Amano: "A charge simulation method for numerical conformal mapping onto circular and radial slit domains" SIAM Journal on Scientific Computing.
• [Publications] T.Inoue: "Algorithm for computing an inverse function of conformal mapping by fundamental solution method" 情報処理学会論文誌. 38-2. 377-379 (1997)
• [Publications] 井上哲男: "数値等角写像に対する代用電荷法による非有界な領域におけるDirichlet問題への応用" 電気学会論文誌C. Vol.117-C(No.6). 727-731 (1997)
• [Publications] T. Inoue: "New charge simulation method numerical conformal mapping of ring domains" Japan Journal of Industrial and Appplied Mathematics. 14-2. 295-301 (1997)
• [Publications] T. Inoue: "The interpolating approximation of smooth functions on an interval by harmonic functions" 情報処理学会. 38-8. 1659-1661 (1997)
• [Publications] 井上哲男: "内部2次元ディリクレ問題に関する新しいスキームによる代用電荷法の数値解析" 電気学会論文誌C. Vol.117-C(No.11). 1540-1546 (1997)
• [Publications] T. Inoue and K. Amano: "Errors relation between real and imaginary parts of numerical conformal mappings in charge simulation method" Theoretical and applied mechanics. 46. 331-340 (1997)
• [Publications] 井上哲男: "代用電荷法における逆等角写像のポテンシャル論的スキーム" 数理解析研究所講究録. 1016. 68-76 (1997)
• [Publications] T. Inoue: "A conformal mapping of Jordan domains" Abstracts Amer.Math.Soc.18-1. (1997)
• [Publications] T. Inoue: "Algorithm for charge simulation method of exterior Dirichlet problem" Abstracts Amer.Math.Soc.18-2. (1997)
• [Publications] Y. Imayoshi: "A remark on Poincare and Bergman metrics,and harmonic and holomorphic maps on a Riemann surface" Proc.5th Internat.Conf.on Finite or Infinite Dimensional Complex Analysis,Beijing,China,1997.
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• [Publications] S. Saitoh: "Pitman Research Notes in Math. 369,Addison Wesley Longman" Integnal transforms, reproducing kernels and their applications, 197 (1997)
• [Publications] 今吉洋一: "サイエンス社," 複素関数概説, 195 (1997)