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Sharp upper diameter bounds for compact shrinking Ricci solitons (2008.02893v2)
Published 6 Aug 2020 in math.DG
Abstract: We give a sharp upper diameter bound for a compact shrinking Ricci soliton in terms of its scalar curvature integral and the Perelman's entropy functional. The sharp cases could occur at round spheres. The proof mainly relies on a sharp logarithmic Sobolev inequality of gradient shrinking Ricci solitons and a Vitali-type covering argument.
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