# Harmonic maps with prescribed singularities and applications in general relativity

## TL;DR

This paper establishes existence and uniqueness results for harmonic maps with prescribed singularities into non-positively curved spaces and explores their applications in general relativity.

## Contribution

It provides a general theoretical framework for harmonic maps with singularities and surveys their relevance to problems in general relativity.

## Key findings

- Proved existence and uniqueness of harmonic maps with prescribed singularities.
- Applied harmonic map theory to specific problems in general relativity.
- Surveyed various applications of harmonic maps in gravitational physics.

## Abstract

This paper presents a general existence and uniqueness result for harmonic maps with prescribed singularities into non-positively curved targets, and surveys a number of applications to general relativity. It is based on a talk delivered by the author at The 11th Mathematical Society of Japan Seasonal Institute, The Role of Metrics in the Theory of Partial Differential Equations.