# Partial regularity of harmonic maps from Alexandrov spaces

## TL;DR

This paper proves that harmonic maps from finite-dimensional Alexandrov spaces to smooth Riemannian manifolds are Lipschitz continuous, confirming a conjecture and extending previous methods.

## Contribution

It establishes the Lipschitz regularity of harmonic maps from Alexandrov spaces, solving a longstanding conjecture and extending existing proof techniques.

## Key findings

- Harmonic maps from Alexandrov spaces are Lipschitz continuous.
- The conjecture of F. H. Lin is confirmed.
- The proof extends Huang-Wang's argument.

## Abstract

In this paper, we prove the Lipschitz regularity of continuous harmonic maps from an finite dimensional Alexandrov space to a compact smooth Riemannian manifold. This solves a conjecture of F. H. Lin in \cite{lin97}. The proof extends the argument of Huang-Wang \cite {hua-w10}.