Abstract: Motivated by stationary vacuum solutions of the Einstein field equations, we study singular harmonic maps from domains of 3-dimensional Euclidean space to the hyperbolic plane having bounded hyperbolic distance to Kerr harmonic maps. In the degenerate case, we prove that every such harmonic map admits a unique tangent harmonic map at the extreme black hole horizon. The possible tangent maps are classified and proved to be integrable. Expansions in the asymptotically flat end are presented. These results, together with those of Li-Tian and Weinstein around 1990, provide a complete regularity theory for such harmonic maps prescribed singularities on $z$-axis. This is joint with Q. Han, M. Khuri and G. Weinstein.
Speaker: Jingang Xiong received his PhD from Beijing Normal University in 2012. After finishing a two-year postdoc at BICMR, he returned back to BNU as a lecturer and he has been a full professor since 2020. He is interested in geometric PDEs and nonlinear analysis.
ID: 841 8136 2356