幾何学的複素解析学とその応用

• Project/Area Number: 06302009
• Research Category: Grant-in-Aid for Co-operative Research (A)
• Allocation Type: Single-year Grants
• Research Field: 解析学
• Research Institution: Kanazawa University
• Principal Investigator: 藤本 坦孝 金沢大学, 理学部, 教授 (60023595)
• Co-Investigator(Kenkyū-buntansha): 渡辺 公夫 筑波大学, 数学系, 助教授 (50015913) ; 竹腰 見昭 大阪大学, 理学部, 助教授 (20188171) ; 森 正気 山形大学, 教養部, 教授 (80004456) ; 鈴木 正昭 富山大学, 理学部, 教授 (10037236) ; 鈴木 昌和 九州大学, 数理学研究科, 助教授 (20112302)
• Project Period (FY): 1994
• Project Status: Completed (Fiscal Year 1994)
• Budget Amount: ¥4,300,000 (Direct Cost: ¥4,300,000); Fiscal Year 1994: ¥4,300,000 (Direct Cost: ¥4,300,000)
• Keywords: 極小曲面 / ネファンリンナ理論 / ガウス写像 / 双曲型空間 / 固有正則写像 / ベルグマン核 / 完備ケーラー多様体 / 擬凸性

Research Abstract

本科研費の援助の下で,3月下旬開催の国際研究集会「幾何学的複素解析」の準備会として,九州大学及び富山大学に於いて研究集会を行い,その他にも小グループ間の研究連絡や情報交換会等を行って,以下の通りの研究成果を得た.
研究代表者藤本は,極小曲面の値分布論的性質を研究し,複素平面に定義域を持つ極小曲面に対するBeckenbachの与えた値分布論を,放物型Riemann面を定義域とする極小曲面の場合に拡張した.関連して,梶原壌二は,極小曲面に近い曲面のガウス写像の擬等角性を調べた.野口潤次郎は,複素射影空間内の高次数双曲的超曲面の存在を示すと共に,値分布論の第2主定理を関数体上の場合に確立し,方程式の有理数解の有限性の問題に応用した.神保敏弥及び坂井章は,C^<12>の全実集合を一成分とする直積集合上の関数の整関数による近似問題を研究した.浜田英隆は,或2次元のラインハルト領域の固有正則写像及び球の間の固有正則写像で平行な超平面上線形であるものを全て決定した.阿部誠は,正値正則直線束をもつ或種の擬凸領域の直線束凸性について研究した.梅野高司は,スタイン多様体をファイバーとするファイバー空間上で,ファイバー上正則なC^∞形式の芽の層のコホモロジー同型定理を与え,トロイダル群の研究に応用した.西原賢は,局所凸空間のリーマン領域から複素リー群への正則写像に対してレヴィの問題を研究し,竹腰見昭は,完備ケーラー多様体上で有界な多重劣調和関数を調べ,標準直線束の固有正則写像による高次順像層のスペクトル系列の退化に関して研究した。田島慎一は,接Chauchy‐Riemann複体のコホモロジー群を調べ,風間英明は,弱擬凸多様体上の正則直線束の切断の関数論的性質を研究し,金丸忠義は,C^nの有界領域からC^n内への単射正則写像の凸性と星型性を調べると共に,バーグマン核を用いて等質有界領域からそれ自身への正則写像に対する歪曲定理を得た.

Research Products

• [Publications] M.Abe: "A generalization of Yasuoka's theorem on the complete Kahler exhaustion" Proc.of 2nd Korean-Japanese Col.1-5 (1994)
• [Publications] M.Abe and H.Hamada: "On the open set exhausted by complete Kahler open sets in a Stein space with isolated singularities" Proc.of 2nd Korean-Japanese Col.7-13 (1994)
• [Publications] M.Abe: "On the line bundle convexity of a totally pseudoconvex open set" Complex Variables Theory Appl.26. 283-290 (1995)
• [Publications] M.Adachi: "Continuation of holomorphic functions from subvarieties to pseudoconvex domains" Kobe J.Math.11. 33-47 (1994)
• [Publications] K.Adachi: "Extending real analytic functions from boundaries of subvarieties to convex domains" Proc.of 2nd Korean-Japanese Col.15-21 (1994)
• [Publications] H.Fujimoto: "Nevanlinna theory for minimal surfaces of parabolic type" Kodai Math.J.(1995)
• [Publications] T.Jimbo and A.Sakai: "Peak interpolation sets of A^∞ for certain nonsmooth domains" Kobe J.Math.(1995)
• [Publications] J.Kajiwara: "Gauss maps of nearly minimal surfaces" Complex Variables. 27. 353-357 (1994)
• [Publications] J.Kajiwara: "Real zeros of holomorphic functions with parameters-III:Surfaces associated to parameters" Proc.of 2nd Korean-Japanese Col.109-115 (1994)
• [Publications] T.Kanemaru: "Distortions related to the Bergman kernel function" Proc.of 2nd Korean-Japanese Col.67-69 (1994)
• [Publications] H.Kazama and T.Ohta: "Existence theorem,imbedding theorem and remark on vanishing theorem on weakly pscudoconvex complex spuecs" Proc.of 2nd Korean-Japanese Col.265-269 (1994)
• [Publications] K.Masuda and J.Noguchi: "A construction of hyperbolic hypersurfaces of P^n(C)" Selected Papers on Geometric Analysis. 53-79 (1994)
• [Publications] H.Hamada: "On proper holomorphic maps between some Reinhardt domains" Proc.of 2nd Korean-Japanese Col.7-13 (1994)
• [Publications] H.Hamada: "Proper holomorphic mapping between balls which are linear on parallel hyperplanes" Bull.Kyushu Kyoritsu Univ.Fac.Engi.19. (1995)
• [Publications] T.Honda: "The solutions of the ∂-operator on an infinite dimensional pseudoconvex domains" Proc.of 2nd Korean-Japanese Col.37-50 (1994)
• [Publications] K,Ikeda: "The Poisson structure on the coordinate ring of discrete Lax operator and Toda Lattice equation" Advances in applied mathematics. 15. 379-389 (1994)
• [Publications] K.Ikeda: "The commutativity of quantized first and higher order Hamiltonians" Journal of Physics A:Maht.Gen.27. 5969-5977 (1994)
• [Publications] T.Jimbo and A.Sakai: "Peak interpolation sets of A^∞" Proc.of 2nd Korean-Japanese Col.67-69 (1994)
• [Publications] S.Tajima: "On the local solvability of the tangential Cauchy-Riemann system" Proc.of 2nd Korean-Japanese Col.179-184 (1994)
• [Publications] S.Tajima and M.Uchida: "On some integral representation formulas for the delta-function" Proc.of 2nd Korean-Japanese Col.179-184 (1994)
• [Publications] K.Takegosi: "A degeneration of Leray spectral sequence for canonicla sheaves tensorized with Nakano semi-positive vector bundles by proper Kahler morphisms" Proc.of 2nd Korean-Japanese Col.2. 193-202 (1994)
• [Publications] K.Takegoshi: "Higher direct images of canonical sheaves tensorized with semi-positive vector bundle by proper Kahler morphisms" Math.Ann.(1995)
• [Publications] H.Tsuji: "On invariant measures on complex manifolds and Kobayashi's conjecture" Selected Papers on Geo.Anal of Sev.Comp.Var.177-184 (1995)
• [Publications] T.Umeno: "de Rham cohomology of holomorphic fiber spaces" Proc.of 2nd Korean-Japanese Col.2. 243-249 (1994)
• [Publications] T.Ohsawa: "On the extensions of L^2 holomorphic functions III, negligible weights" Math.Z.(1995)
• [Publications] T.Ohsawa: "On the extension of L^2 holomorphic functions IV, a new density concept" Geometry and analysis on complex manifolds,World Scientific. 157-170 (1994)
• [Publications] F.Sakanishi: "On a metric induced by the quasiconformal diffeomeorphism" Proc.of 2nd Korean-Japanese Col.149-153 (1994)
• [Publications] F.Sakanishi: "Boundary behavior of the quasiconformal diffeomorphism" Proc,of 2nd Korean-Japanese Col.155-162 (1994)
• [Publications] S.Tajima: "Bochner‐Martinelli cohomology classes and tangential Cauchy-Riemann coplexes with coefficents in microfunctions" Kyushu J.of Math.48. 43-54 (1994)
• [Publications] S.Tajima and M.Uchida: "Integral fromula for the resolution of a palne curve singularity" Funkcialaj Ekuacioj. 37. 229-239 (1994)
• [Publications] K.Nishihara: "On the indicator of growth of entire functions of exponential type in infinite dimensional spaces and the Levi problem in infinite dimensional projevtive spaces" Portugaliae Mathematica. (1995)
• [Publications] K.Nishihara: "On the Levi problem for holomorphic mappings of Riemann domains over infinite dimensional spaces into a complex Lie group" Res.Bull.Fukuoka Inst.Technology. 26. 151-161 (1994)
• [Publications] K.Nishihara: "∂-equations on infinite dimensional Grassmann manifolds" Proc.of 4th Inter.Col.on Diff.Eq.18-23 (1993)
• [Publications] K.Nishihara: "On te indicator of growth of entire functions of exponential type in infinite dimensional" Proc,of 2nd Korean-Japanese Col.27-29 (1994)
• [Publications] J.Noguchi: "Some topics in Nevanlinna-theory,hyperbolic manifolds and Diophantine geometry" Geometry and Analysis on Complex Manifolds. (1995)
• [Publications] J.Noguchi: "A short analvtic proof of closedness of logarithmic forms" Kodai Math.J.(1996)
• [Publications] J.Noguchi: "Nevanlinna-Cartan theory over function fields and a Diophantine equation" Selected Papers on Geometric Analysis. 97-119 (1994)
• [Publications] T.Ohsawa and K.Diederich: "Genaral continuity principles for the Bergman kernel" International J.Math.5. 189-199 (1994)
• [Publications] T.Ohsawa and K.Diederich: "An estimate for the Bergman distance on pseudoconvex domains" Ann,Math.(1995)
• [Publications] T.Ohsawa: "On the analytic structure of certain infinite dimansional Teichmuller spaces" Selected papers on the Geometric Analysis. (1994)
• [Publications] T.Ohsawa: "On a class of (-3,1)-exceptional P^1" Complex Analysis and geometry. (1995)
• [Publications] T.Ohsawa: "Addendum to“On the Bergman kernel of huyperconvex domains"" Nagoya Math.J.137. (1995)