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RESEARCH ON COMPLEX ANALYSIS BY GROUP THEORETIC AND GEOMETRIC METHOD

群论与几何方法的复分析研究

基本信息

批准号：
12640167
负责人：
TAKEUCHI Shigeru
金额：
$ 1.92万
依托单位：
GIFU UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2000
资助国家：
日本
起止时间：
2000 至 2003
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-12640167/
关键词：
CR LIE GROUP ACTION CR LIE ALGEBRA LINEAR CR LIE GROUP CR ADAPTED COMPLEXIFICATION CATEGORY OF GROUP ACTION CR GROUP MANIFOLD CATEGORICAL COMPLEXIFICATION CR REAL FORM CR実形式無限次元CRベクトル空間双対カテゴリー複素化圏論的単射圏論的像圏論的全射 CR多様体 C

项目摘要

(1)Takeuchi studied the basic relations of the CR structures of the manifolds and its adapted complexifications or CR forms from categorical points of view, and obtained some affirmative results on epics, monics and images in the CR category. He also studied the serious situations in mathematics education not only in Japan but also world wide, e.g in Latin America and south east Asia.(2)Kazuyuki Hatada studied metric properties of geometric simplices and generalized the formula among the ditance of the point in a triangle from the vertices to higher dimensional simplices. He also studied p-adic properties of p-adic limits of sequences defined by norms and traces of algebraic integers and p-adic modular forms.(3)Shimizu studied the holomorphic vector fields of tube domains and obtained the criterion of the their completeness, clarified the their Lie algebra structures solved the holomorphic equivalence problem affirmatively and gave a characterization of a certain type of Stein manifolds by their automorphism groups.(4)Fujimoto proved if a nonsingular projective 3-fold of non-negative Kodaira dimension admits a non trivial endomorphism, its finite unramified covering to be a smooth family of abelian varieies and gave a sufficient condition for an endornorphism of the product manifold of a minimal variety X with a non minimal one Y to split into product for the case of 3-dimensional Y.(5)Aiki studied the models for shape memory alloys described by subdifferentials of indicator functions, obtained the existence and uniqueness of the solution of one-phase Stefan problems with nonlinear boundary conditions described by maximal monotone operators.(6)Yamada, analyzing the Carleson inequality, obtained more general results than before and introduced the similar condition corresponding to the (A_p) one in Bergman space, which is the Banach space of harmonic functions.

（1）Takeuchi从范畴的角度研究了流形的CR结构与其适应复化或CR形式之间的基本关系，得到了CR范畴中Epics、Monics和Image的一些肯定结果。他还研究了严重的情况下，数学教育不仅在日本，而且在世界各地，例如在拉丁美洲和东南亚。（2）Kazuyuki Hatada研究了几何单形的度量性质，并将三角形中点距顶点的距离公式推广到高维单形。他还研究了p-adic属性的p-adic限制序列定义的规范和痕迹的代数整数和p-adic模块化的形式。（3）Shimizu研究了管域的全纯向量场，得到了它们完备性的判别准则，阐明了它们的李代数结构，肯定地解决了全纯等价问题，并给出了一类Stein流形的自同构群的刻画。（4）Fujimoto证明了非负科代拉维数的非奇异射影3-fold若有非平凡的自同态，则其有限非分歧覆盖是阿贝尔簇的光滑族，并给出了极小簇X与非极小簇Y的乘积流形的自同态分裂为乘积的充分条件。（5）Aiki研究了用指示函数的次微分描述的形状记忆合金模型，得到了用极大单调算子描述的具有非线性边界条件的单相Stefan问题解的存在唯一性。（6）Yamada在分析Carleson不等式的基础上，得到了更一般的结果，并在调和函数的Banach空间Bergman空间中引入了与（A_p）不等式相对应的类似条件。