RESEARCH ON COMPLEX ANALYSIS BY GROUP THEORETIC AND GEOMETRIC METHOD

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(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.