Gradient flow of the norm squared of a moment map over Kahler manifolds

Aijin Lin; Liangming Shen

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arXiv · 1802.09314

Gradient flow of the norm squared of a moment map over Kahler manifolds

Aijin Lin·Liangming Shen

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Abstract

Inspired by Wilkin's work [23, 24] on Morse theory for the moduli space of Higgs bundles, we study the moduli space of gauged holomorphic maps by a heat flow approach in the spirit of Atiyah and Bott in a series of papers. In this paper, applying the method of Hong [9], we establish the global existence of smooth solutions of the gradient ow equations of the vortex functional over a compact Kahler manifold.

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Aijin Lin, Liangming Shen. 2018-02-26. Gradient flow of the norm squared of a moment map over Kahler manifolds. https://arxiv.org/abs/1802.09314

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