Existence of approximate Hermitian-Einstein structures on semi-stable Higgs bundles
JiaYu Li, Xi Zhang
TL;DR
This paper proves that semi-stable Higgs bundles over compact Kähler manifolds admit approximate Hermitian-Einstein structures, utilizing Donaldson's heat flow to establish the existence of such structures.
Contribution
It demonstrates the existence of approximate Hermitian-Einstein structures on semi-stable Higgs bundles using Donaldson's heat flow, extending previous results in the field.
Findings
Semi-stability implies existence of approximate Hermitian-Einstein structures.
Utilizes Donaldson's heat flow method.
Applicable to Higgs bundles over compact Kähler manifolds.
Abstract
In this paper, using Donaldson's heat flow, we show that the semi-stability of a Higgs bundle over a compact K\"ahler manifold implies the existence of approximate Hermitian-Einstein structure on the Higgs bundle.
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Taxonomy
TopicsGeometry and complex manifolds · Algebraic Geometry and Number Theory · Geometric Analysis and Curvature Flows