Gravitational instantons and harmonic maps
数学专题报告
报告题目(Title)：Gravitational instantons and harmonic maps
报告人(Speaker)：Mingyang Li (Stony Brook University)
地点(Place)：ZOOM ID：932 5027 7484 PWD：399689
时间(Time)：2026年3月13日（周五）9:30-10:30
邀请人(Inviter)：熊金钢
报告摘要
Axisymmetric stationary black holes in general relativity admit a classical reduction to axisymmetric harmonic maps into the hyperbolic plane H^2. In a Riemannian analogue, four-dimensional Ricci-flat metrics with torus symmetry can likewise be described locally by harmonic maps to H^2, now subject to an additional tameness condition that encodes regularity of the metric. We study such harmonic maps and application includes a construction of infinitely many new complete, asymptotically flat, Ricci-flat 4-manifolds with arbitrarily large second Betti number b_2. If time permits, I will also briefly describe how the same framework can be run in the opposite direction: in low degree one can classify such tame axisymmetric harmonic maps based on our study of gravitational instantons. Joint work with Song Sun.
* This PDE seminar is co-organized with Tianling Jin at HKUST and Juncheng Wei at CUHK. See the seminar webpage: https://www.math.hkust.edu.hk/~tianlingjin/PDEseminar.html
