Project/Area Number  02452004 
Research Category 
GrantinAid for Scientific Research (B).

Research Field 
代数学・幾何学

Research Institution  Keio University 
Principal Investigator 
OBATA Morio Keio University Professor, 理工学部, 教授 (90087015)

CoInvestigator(Kenkyūbuntansha) 
MAEDA Yoshiaki Keio University Associate Professor, 理工学部, 助教授 (40101076)
前島 信 慶応義塾大学, 理工学部, 教授 (90051846)
ITO Yuji Keio University Professor, 理工学部, 教授 (90112987)
TANAKA Hiroshi Keio University Professor, 理工学部, 教授 (70011468)
菊池 紀夫 慶応義塾大学, 理工学部, 教授 (80090041)
ISHII Ippei Keio University Associate Professor (90051929)
KANAI Masahiko Keio University Assistant Professor (70183035)

Project Fiscal Year 
1990 – 1991

Project Status 
Completed(Fiscal Year 1991)

Budget Amount *help 
¥4,600,000 (Direct Cost : ¥4,600,000)
Fiscal Year 1991 : ¥2,100,000 (Direct Cost : ¥2,100,000)
Fiscal Year 1990 : ¥2,500,000 (Direct Cost : ¥2,500,000)

Keywords  YangMills fields / Harmonic maps / stability for the variational problem / operator algebra / selfsimilarity / fractals / knot theory / Markov process / ヤングミルズ場 / 調和写像 / 変分問題の安定性 / 作用素環 / セルフシミラリティ / フラクタル / 結び目理論 / マルコフ過程 
Research Abstract 
Through 1991 year, we invited. many researchers from the wide subjects in mathematics to ge+ new informations and current results. We arranged seminars and discuss with them mainly at Keio University. Throughtout the discussions, some results have been made by coorperators in our group of this projects. Namely, the existence of the global weak solutions for the YangMills gradient flow and the variational problems for the Harmaonic maps were studied by Maeda, Kikuch and Tani. They established the basic problems and could getaffirmative answers. Now, they are going to study these in more details. Kanai and Nakada got some results on the problems on the number theory and the rigidity of the group actions on nonpositive manifolds from the ergodic theoretical points of view. Ishii is given some topological invariants for 3manifolds by the study of knots and links. Tanaka gives the new ideas for studying the properties on manifolds by using the stochastic analysis.
