Asymptotic analysis for harmonic maps with prescribed singularities

The PDE & Analysis seminar covers topics in PDE and analysis.

schedule Date & time
20 Nov 2023 | 2 - 3:20pm
person Speaker


Prof Qing Han, University of Notre Dame
next_week Event series
contact_support Contact

Content navigation



Motivated by studies of axially symmetric stationary solutions of the Einstein vacuum equations in general relativity, we study singular harmonic maps from the 3-dimensional Euclidean space to the hyperbolic plane, with prescribed singularities. We prove that every such harmonic map has a unique tangent map at the black hole horizon and the harmonic map depends on the location of the black hole smoothly. The harmonic map equation restricted to the unit sphere has a singularity at the north and south poles. The collection of parameters representing the conical singularities in the tangent map determines a flow along which the reduced energy of the harmonic map is decreasing. This leads to an explicit and optimal lower bound for the ADM mass in terms of the total angular momentum, in asymptotically flat, axially symmetric, and maximal initial data sets for the Einstein equations with multiple black holes. The talk is based on joint work with Marcus Khuri, Gilbert Weinstein, and Jingang Xiong.



145 Hanna Neumann Building, room 1.33

-35.275905261234, 149.1191726

Upcoming events in this series

Abstract technology background with connected dots
6 Dec 2023 | 10:30am - 12pm
Abstract technology background with connected dots
5 Dec 2023 | 1:30 - 2:30pm

The PDE & Analysis seminar covers topics in PDE and analysis.

View the event