Geodesic Rays in the Donaldson--Uhlenbeck--Yau Theorem

TL;DR

This paper presents new proofs of key implications in the Donaldson--Uhlenbeck--Yau theorem using geodesic rays of Hermitian metrics, inspired by recent developments related to the Yau--Tian--Donaldson conjecture.

Contribution

The paper introduces novel proof techniques for the Donaldson--Uhlenbeck--Yau theorem based on geodesic rays, connecting geometric analysis with stability concepts.

Findings

New proofs of two implications in the theorem

Use of geodesic rays of Hermitian metrics

Connection to Yau--Tian--Donaldson conjecture

Abstract

We give new proofs of two implications in the Donaldson--Uhlenbeck--Yau theorem. Our proofs are based on geodesic rays of Hermitian metrics, inspired by recent work on the Yau--Tian--Donaldson conjecture.