RESEARCH ON COMPLEX ANALYSIS BY GROUP THEORETIC AND GEOMETRIC METHOD

(1)Takeuchi从范畴的角度研究了流形的CR结构与其适应的复合化或CR形式之间的基本关系，得到了关于CR范畴中的史诗、单调和意象的一些肯定的结果。他还研究了不仅在日本，而且在世界范围内，例如拉丁美洲和东南亚数学教育中的严重情况。(2)Hatada Kazuyuki Hatada研究了几何单纯的度量性质，并将三角形中点从顶点到高维单纯的距离公式推广到高维单纯形。(3)清水研究了管域的全纯向量场，得到了它们的完备性的判据，阐明了它们的李代数结构，肯定地解决了全纯等价问题，并用它们的自同构群刻画了一类Stein流形。(4)Fujimoto证明了非负Kodaira维的一个非奇异射影3重存在非平凡自同态，(5)Aiki研究了用指标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分析了Bergman空间中Carleson不等式，得到了更一般的结果，并引入了与(A_P)相对应的条件。它是调和函数的Banach空间。

(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.