Geometric analysis for ideal boundaries of product manifolds, and the study of harmonic maps and Einstein metrics

2014 Fiscal Year Final Research Report

• Project/Area Number: 24654009
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Geometry
• Research Institution: Tokyo Institute of Technology (2013-2014); Tohoku University (2012)
• Principal Investigator: AKUTAGAWA Kazuo 東京工業大学, 理工学研究科, 教授 (80192920)
• Co-Investigator(Renkei-kenkyūsha): KUMURA Hironori 静岡大学, 大学院理学研究科, 准教授 (30283336) ; AIYAMA Reiko 筑波大学, 大学院・数理物質科学研究科, 講師 (20222466)
• Research Collaborator: MAZZEO Rafe Stanford University (USA), Department of Mathematics ; MATSUMOTO Yoshihiko 東京工業大学, 大学院理工学研究科, 学振PD
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 調和写像 / アインシュタイン計量 / 理想境界 / 直積多様体 / 幾何解析 / 国際研究者交流 / 国際情報交換 / 多国籍

Outline of Final Research Achievements

On this research theme, I have obtained the following results: (1) the finiteness and infiniteness theorems of discrete spectrum of the Schrodinger operators on noncompact manifolds， (2) the existence and uniqueness theorems of the Dirichlet problem at infinity for harmonic maps between asymptotic hyperbolic manifolds， (3) the representational formula and halfspace theorem for minimal Legendrian surfaces in the 5-dimensional Heisenberg group， (4) the value distribution theorem for the Gauss maps of minimal Lagrangian surfaces in the complex 2-space.

Free Research Field

数物系科学