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arXiv · 1410.5150

Stabilities of homothetically shrinking Yang-Mills solitons

Zhengxiang Chen·Yongbing Zhang
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Abstract

In this paper we introduce entropy-stability and F-stability for homothetically shrinking Yang-Mills solitons, employing entropy and second variation of $\mathcal{F}$-functional respectively. For a homothetically shrinking soliton which does not descend, we prove that entropy-stability implies F-stability. These stabilities have connections with the study of Type-I singularities of the Yang-Mills flow. Two byproducts are also included: We show that the Yang-Mills flow in dimension four cannot develop a Type-I singularity; and we obtain a gap theorem for homothetically shrinking solitons.

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Zhengxiang Chen, Yongbing Zhang. 2014-12-16. Stabilities of homothetically shrinking Yang-Mills solitons. https://arxiv.org/abs/1410.5150

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