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

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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.
LaTeX2e, 7 pages. To appear in Arch. Math. Revised version improves result to also cover positive case

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Differential Geometry, Functional Analysis, 53C21, 58J50

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http://salesiana.dossiersoluciones.com/handle/123456789/117818

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0610130
 http://arxiv.org/abs/math/0610130

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arXiv