报告时间：2024年6月21日 9：00开始
报 告 人：Hao Fang（University of Iowa）
报告地点：9-113
报告题目：New Monge-Ampère Equations in bi-Hermitian Geometry
报告摘要：We report some recent progress in bi-Hermitian geometry. This is a joint work with Josh Jordan. We introduce complex surfaces with split tangent, which contain two important classes of type VII surfaces in the classification theory of Enriques-Kodaira. The split tangent structure is naturally related to the Bismut Ricci curvature of pluri-closed bi-Hermtian metrics. We pose several Monge-Ampère type PDEs that are new in both geometry and PDE theories. We establish certain solvability theorems under proper geometric settings.
As applications, on surfaces with split tangent, we solve the prescribing Bismut-Ricci problems. For primary Hopf surfaces, we prove a uniformization theorem, linking all pluriclose bi-Hermitian metrics to Streets-Usinovskiy metrics. On Hopf surfaces, we also provide a second type of canonical metrics that are associated to a special Calabi-Yau type problem. On Inoue surfaces of type $M$, we establish classes of canonical metrics due to various geometric criteria.
报告人简介：Hao Fang，University of Iowa, Associate Professor，博士毕业于Princeton University。主要从事微分几何、几何分析等领域的研究，相关研究成果发表在Invent. Math., J. Differential Geom., Adv. Math., J. Reine Angew. Math. 等国际学术期刊上。
