Gromov-Hausdorff limits and complex analytic geometry

2016 Fiscal Year Final Research Report

• Project/Area Number: 26610013
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Geometry
• Research Institution: The University of Tokyo
• Principal Investigator: Futaki Akito 東京大学, 大学院数理科学研究科, 教授 (90143247)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: グロモフ・ハウスドルフ極限 / ケーラー多様体 / K 安定性 / アインシュタイン計量

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.

Free Research Field

数物系科学