The heat flow for Kahler fibrations
Aijin Lin
TL;DR
This paper proves the global existence of smooth solutions to the heat flow for Yang-Mills-Higgs functionals on Kahler fibrations and offers a new proof of a key inequality in the Hitchin-Kobayashi correspondence.
Contribution
It introduces a heat flow approach to establish the key inequality in the Hitchin-Kobayashi correspondence for Kahler fibrations.
Findings
Global existence of smooth heat flow solutions on Kahler fibrations
New proof of the key inequality in Mundet's Hitchin-Kobayashi theorem
Application of heat flow technique to complex geometric problems
Abstract
We establish global existence of smooth solutions to heat flow for Yang-Mills-Higgs functional on Kahler fibrations. As an application, we give a new proof of the key inequality for Mundet's Hitchin-Kobayashi correspondence theorem using the heat flow technique.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Advanced Operator Algebra Research