Scalar curvature bound and compactness results for Ricci harmonic solitons

Wu, Guoqiang

doi:10.1090/proc/13410

Scalar curvature bound and compactness results for Ricci harmonic solitons
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by Guoqiang Wu PDF

Proc. Amer. Math. Soc. 146 (2018), 3473-3483 Request permission

Abstract:

In this paper, we study the gradient Ricci harmonic soliton. For noncompact gradient shrinking Ricci harmonic solitons, we prove that the scalar curvature has at most quadratic decay. Given some curvature conditions, we prove that these shrinking solitons must be compact. In two dimensions, we can get similar results with weaker assumptions.

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