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幾何学的複素解析学とその応用

几何复形分析及其应用

基本信息

批准号：
06302009
负责人：
藤本坦孝
金额：
$ 2.75万
依托单位：
Kanazawa University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Co-operative Research (A)
财政年份：
1994
资助国家：
日本
起止时间：
1994 至无数据
项目状态：
已结题

项目摘要

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.

Under the support of this research fund, the preparatory meeting for the international research conference "Complex Element Analysis of Geometry" was held in late March. Kyushu University and Toyama University conducted research meetings in the middle of the year, and other research contacts and information exchange meetings were held. The following research results were obtained. Fujimoto, a representative researcher, studies the properties of the value distribution theory of minimal surfaces. Beckenbach and the value distribution theory of complex prime planes are related to the domain of minimal surfaces. The relationship between the two, minimal surface, near middle surface, and quasi-equiangular property of the image is adjusted. Noguchi Junjiro, the existence of hyperbolic hypersurfaces of high degree in complex prime projective spaces, the establishment of the second principal theorem of the theory of value distribution, and the application of the problem of finiteness of rational solutions of equations. Minho and Sakai Akira are studying the approximation problem of the integral number of relations on the set of direct products of a complete set of C^<12>Hidetaka Hamada, or 2-D domain inherent regular image and sphere inherent regular image parallel hyperplane linear shape Abe seiko, positive value regular straight line bundle or species of quasi-convex field of straight line bundle convexity. Takashi Ueno is an expert in the study of multi-dimensional space, multi-dimensional space and multi-dimensional space. Nishihara Kenji, the local convex space of the domain of the complex prime group of regular writing problems related to the study of the problem, Takewaka Miaki, complete multi-dimensional bounded multi-inferior and correlation adjustment, standard straight beam of the inherent regular writing of the high-order image layer related to the study of the degradation of the series Tajima Shin Ichi, Joining Chauchy-Riemann Complex, Kauma Hideaki, and Weakly Quasiconvex Polymorph, studied the properties of the number theory of regular straight line bundle on the cut, Kanemaru Tadashi, Joined Chauchy-Riemann Complex, Joined Chauchy-Riemann Complex, Kauma Hideki, and Weakly Quasiconvex Polymorph, Kanemaru Tadashi, Joined Chauchy-Riemann Complex, Joined Chauchy-Riemann Complex, Kauma Hideki, and Kanemaru Tadashi, Joined C ^n bounded domain, Joined C ^n inner domain, Joined C^n inner domain, Joined Chauchy-Riemann Complex, Joined Chauchy-Riemann Complex, Joining Chauchy-Riemann Complex, Kauma Hideki, Joshi Kazuma Hideki, and Kanemaru Tadashi, Kanemaru Tadashi, obtained the distortion theorem of regular image on C ^n inner domain.