The Flow of Gauge Transformations on Riemannian Surface with Boundary

TL;DR

This paper studies gauge transformations of metric G-bundles on Riemannian surfaces with boundary, proving existence and long-term behavior of solutions using heat flow methods.

Contribution

It introduces a heat flow approach to analyze gauge transformations on surfaces with boundary, establishing existence results for generalized solutions.

Findings

Proved local and long-term existence of solutions.

Applied heat flow techniques to gauge transformations.

Extended analysis to surfaces with boundary.

Abstract

We consider the gauge transformations of a metric $G$-bundle over a compact Riemannian surface with boundary. By employing the heat flow method, the local existence and the long time existence of generalized solution are proved.