We will present a general theory of existence and uniqueness for harmonic maps with prescribed singularities into Riemannian manifolds with non-positive curvature. The singularities are prescribed along submanifolds of co-dimension 2. This result generalizes one from 1996, and is motivated by a number of recent applications in general relativity including:
* a lower bound on the ADM mass in terms of charge and angular momentum for multiple black holes;
* a lower bound on the ADM mass in terms of horizon area and angular momentum (Penrose inequality with angular momentum);
* existence and uniqueness of stationary charged rotating solutions with infinitely many co-rotating black holes along one axis (periodic solutions);
* existence and uniqueness of black holes with exotic topology in higher dimensions.
We present a survey of these applications.
This work includes joint projects with Marcus Khuri and Sumio Yamada. Speaker(s): Gilbert Weinstein (Ariel University, Israel)