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结构及其适应的复杂形式或CR形式之间的基本关系，并对CR范畴中的史诗、monics和象得到了一些肯定的结果。他还研究了日本乃至世界范围内数学教育的严峻形势，例如拉丁美洲和东南亚。(2)Kazuyuki Hatada研究了几何简单体的度量性质，并推广了三角形中点到高维简单体的距离公式。他还研究了由代数整数的范数和迹以及p进模形式定义的序列的p进极限的p进性质。(3)Shimizu研究了管域的全纯向量场，得到了管域完备性的判据，明确了管域的李代数结构，肯定地解决了全纯等价问题，并给出了一类Stein流形的自同构群表征。(4)Fujimoto证明了非负Kodaira维的非奇异射影3重具有非平凡自同态，它的有限非分支覆盖是光滑的阿贝变体族，并给出了在三维Y的情况下极小变体X的积流形与非极小变体Y分裂为积的内同性的充分条件。得到了一类具有极大单调算子描述的非线性边界条件的一相Stefan问题解的存在唯一性。(6)Yamada通过对Carleson不等式的分析，得到了比以前更一般的结果，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。

(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.