Research of Moduli spaces based on various metrics

2016 Fiscal Year Final Research Report

• Project/Area Number: 25400142
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Kagoshima University
• Principal Investigator: OBITSU KUNIO 鹿児島大学, 理工学域理学系, 准教授 (00325763)
• Project Period (FY): 2013-04-01 – 2017-03-31
• Keywords: リーマン面 / モジュライ / ケーラー計量 / 漸近展開

Outline of Final Research Achievements

Main topic of this research is to find out the asymptotic expansion formula for the Weil-Petersson and the Takhtajan-Zograf metrics near the boundary of Moduli spaces of punctured Riemann surfaces. I have improved the former upper bound estimates of the asymptotic behavior of the Takhtajan-Zograf metric. Around 2015, Mazzeo, Swoboda, Melrose, and Zhu obtained the new proofs and some improvements of my previous estimates of the asymptotics of the Weil-Petersson and the Takhtajan-Zograf metrics. I discussed their new approaches with them, and now am working in unifying their and my techniques to get the complete expansion formulas.

Free Research Field

複素解析学