[ Seminar 2021 | Past Seminars | Related conferences etc. ]
| Date: | July 28 (Wed), 2021, 17:00-18:00 |
| Speaker: | Yoshiki Ohima (大島芳樹) (Osaka University) |
| Title: | Ricci平坦計量の崩壊とMonge-Ampere方程式の解のアプリオリ評価 / Collapsing Ricci-flat metrics and a priori estimate for the Monge-Ampere equation |
| Abstract: [ pdf ] |
YauはMonge-Ampere方程式の解のアプリオリ評価を行ってCalabi予想を証明した．
近年ファイバー空間の構造を持つCalabi-Yau多様体
について，底空間のKahler類に崩壊するようなRicci平坦Kahler計量の振舞が
Gross-Tosatti-Zhang等により研究されている．尾高悠志
との共同研究(arXiv:1810.07685)で得られたK3曲面の球面へのGromov-Hausdorff収束も，これらのMonge-Ampere方程式の解の評価に基
づいている．この講演では，微分方程式の解の評価がどのように自然な計量の存
在やGromov-Hausdorff収束を導くかをお話ししたい．
Yau proved the Calabi conjecture by using a priori estimate for the Monge-Ampere equation. Recently, for a Calabi-Yau manifold with a fiber space structure, the behavior of Ricci-flat metrics collapsing to a Kahler class of the base space was studied by Gross-Tosatti-Zhang, etc. The Gromov-Hausdorff convergence of K3 surfaces to spheres obtained by a joint work with Yuji Odaka (arXiv:1810.07685) is also based on those estimates for solutions to the Monge-Ampere equation. In this talk, I would like to discuss how an estimate of solutions to differential equations deduces the existence of canonical metrics and the Gromov-Hausdorff convergence. |
© Toshiyuki Kobayashi