| Budget Amount *help |
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Outline of Final Research Achievements |
I studied the spectral convergence for the Gromov-Hausdorff limits of the sequence of Fano manifolds with Ricci curvature bounded from below. First of all, jointly with Shouhei Honda and Shunsuke Saito, we obtained compactness result for Fano manifolds with Ricci curvature bounded from below. Secondly, we proved the convergence of the spectrum of weighted Laplacian at the Gromov-Hausdorff limit. Thirdly, we obtained a structure theorem for the Lie algebra of all holomorphic vector fields when the limit becomes a Kaehler-Ricci soliton. As a different direction, jointly with Kota Hattori and Hikaru Yamamoto, we extended the earlier work of Huisken to cone manifolds to show the appearance of self-similar solutions of the mean curvature flow.
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