Geometric Analysis Seminar —— Poincaré-Einstein 4-Manifolds with Conformally Kähler Geometry
报告人：刘弘毅 (Princeton University)
时间：2026-04-01 09:00-10:00
地点：online
【摘要】
Poincaré–Einstein metrics play an important role in geometric analysis and mathematical physics, yet constructing new examples beyond the perturbative regime is difficult. In this talk, I will describe a class of four-dimensional Poincaré–Einstein manifolds that are conformal to Kähler metrics. These metrics admit a natural symmetry generated by a Killing field, which reduces the Einstein equations to a Toda-type system. This approach leads to existence and uniqueness results in the case of complex line bundles over surfaces of genus at least one. The construction produces large-scale, infinite-dimensional families of new Poincaré–Einstein metrics with conformal infinities of non-positive Yamabe type. This is joint work with Mingyang Li.
【报告人简介】
Hongyi Liu is currently an instructor at Princeton University. He obtained his Ph.D. at University of California, Berkeley in 2023. His research focuses on differential geometry and geometric analysis.
Zoom: 820 9062 6605 Password: 117123
