New development of inverse spectral problems for singular spaces

2014 Fiscal Year Final Research Report

• Project/Area Number: 24654010
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Geometry
• Research Institution: Kyoto University (2014); University of Tsukuba (2012-2013)
• Principal Investigator: YAMAGUCHI Takao 京都大学, 理学(系)研究科(研究院), 教授 (00182444)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: スペクトル逆問題 / 特異空間

Outline of Final Research Achievements

We have obtained the following mathematical findings as results of this reserach project. (1) By a joint work with Ayato Mitsuishi, we found local Lipschitz homotopy structure of Alexandrov spaces.(2) We observed that there is a possibility of establishing Tataru's unique continuation theorem for waves on the GH-limit spaces of Riemannian manifolds whose Ricci curvatures are uniformly bounded below. (3)We found that considering spectral limits of Schrodinger operators on collapsed surfaces whose curvatures explode to -infinity should be usuful in the study of waves of some quantum graphs.

Free Research Field

微分幾何学