Perelman's invariant, Ricci flow, and the Yamabe invariants of smooth manifolds

Kazuo Akutagawa, Masashi Ishida, Claude LeBrun

Research output: Contribution to journalArticlepeer-review

19 Citations (Scopus)

Abstract

In his study of Ricci flow, Perelman introduced a smooth-manifold invariant called λ. 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 +∞ whenever the Yamabe invariant is positive.

Original languageEnglish
Pages (from-to)71-76
Number of pages6
JournalArchiv der Mathematik
Volume88
Issue number1
DOIs
Publication statusPublished - 2007 Jan

Keywords

  • Conformal geometry
  • Perelman invariant
  • Ricci flow
  • Scalar curvature
  • Yamabe problem

ASJC Scopus subject areas

  • Mathematics(all)

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