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Perelman's Invariant, Ricci Flow, and the Yamabe Invariants of Smooth Manifolds

Kazuo Akutagawa·Masashi Ishida·Claude LeBrun
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Abstract

In his study of Ricci flow, Perelman introduced a smooth-manifold invariant called lambda-bar. We show here that, for completely elementary reasons, this invariant simply equals the Yamabe invariant, alias the sigma constant, whenever the latter is non-positive. On the other hand, the Perelman invariant just equals + infinity whenever the Yamabe invariant is positive.

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Kazuo Akutagawa, Masashi Ishida, Claude LeBrun. 2006-10-17. Perelman's Invariant, Ricci Flow, and the Yamabe Invariants of Smooth Manifolds. https://arxiv.org/abs/math/0610130

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