Regularity for Harmonic - Einstein Equation

TL;DR

This paper proves a regularity theorem for the Harmonic-Einstein Equation and derives a compactness result, primarily using Moser iteration techniques, advancing understanding of solutions' smoothness and limits.

Contribution

It introduces a new regularity theorem for the Harmonic-Einstein Equation and establishes a compactness theorem, applying and extending Moser iteration methods.

Findings

Established regularity for solutions of the Harmonic-Einstein Equation

Proved a compactness theorem for the equation

Utilized Moser iteration techniques extensively

Abstract

We establish a regularity theorem for the Harmonic - Einstein Equation. As a byproduct of the local regularity, we also have a compactness theorem on Harmonic - Einstein equation. The method is mainly the Moser iteration technique which has been used and developed by \cite{BKN89}, \cite{Tian90}, \cite{TV05a} and others.