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

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

2006-10-04

arxiv.org/abs/math/0610130v2

Mathematics

Differential Geometry

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

Scientific paper

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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