Remarks on the Yang-Mills flow on a compact Kahler manifold

Tristan C. Collins; Adam Jacob

Remarks on the Yang-Mills flow on a compact Kahler manifold

Differential Geometry 2013-10-01 v3 Analysis of PDEs

Authors: Tristan C. Collins , Adam Jacob

Abstract

We study the Yang-Mills flow on a holomorphic vector bundle E over a compact Kahler manifold X. We construct a natural barrier function along the flow, and introduce some techniques to study the blow-up of the curvature along the flow. Making some technical assumptions, we show how our techniques can be used to prove that the curvature of the evolved connection is uniformly bounded away from an analytic subvariety determined by the Harder-Narasimhan-Seshadri filtration of E. We also discuss how our assumptions are related to stability in some simple cases.

Keywords

Yang-Mills flow compact Kahler manifold holomorphic vector bundle curvature blow-up Harder-Narasimhan-Seshadri filtration stability

Cite

@article{arxiv.1206.6790,
  title  = {Remarks on the Yang-Mills flow on a compact Kahler manifold},
  author = {Tristan C. Collins and Adam Jacob},
  journal= {arXiv preprint arXiv:1206.6790},
  year   = {2013}
}

Comments

We found a mistake in the proof of Proposition 4. The paper has been completely rewritten. The title and abstract have been altered to reflect the changes. 26 pages

Remarks on the Yang-Mills flow on a compact Kahler manifold

Abstract

Keywords

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