[CvGmt News] Seminari Calcolo delle Variazioni

[depascal at dm.unipi.it]

This is a memo for the talk of this afternoon
Luigi

Perelman's -functional and the stability of Ricci-flat metrics
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   Wednesday, November 25 17 in Sala Riunioni , Dipartimento di Matematica
   Prof. Robert Haslhofer (ETH Zurich) Will speak about:

   Perelman's -functional and the stability of Ricci-flat metrics

   Abstract: Hamilton's Ricci flow can be interpreted as gradient flow of
   Perelman's l-functional on the space of metrics modulo diffeomorphisms.
   In particular, if compact Ricci-flat metrics are dynamically stable
   fixed points of the Ricci flow, then they locally maximize l, and this
   in turn implies that their Lichnerowicz Laplacians have only
   nonpositive eigenvalues. In this talk, I will show that the converse
   implications are also true, provided the premoduli space of Ricci-flat
   metrics is a manifold of prescribed dimension. To prove the local
   maxima result, I use the Ebin-Palais slice theorem and estimate the
   error term in the Taylor expansion of l coming from the third
   variation. To show dynamical stability, I prove a Lojasiewicz-Simon
   type gradient inequality for the Ricci flow and estimate the motion in
   the gauge directions. Similar dynamical stability results have been
   obtained by other authors using the Ricci-DeTurck flow.


You find this news in the cvgmt preprint server: http://cvgmt.sns.it/news/20091125/