[CvGmt News] Seminari Calcolo delle Variazioni
depascal at dm.unipi.it
depascal at dm.unipi.it
Fri Nov 20 12:12:22 CET 2009
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/
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