| Budget Amount *help |
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| 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.
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