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SUMMARY:Dynamical stability and instability of Ricci-flat metrics - Reto M
 ueller (Imperial College)
DTSTART:20130204T150000Z
DTEND:20130204T160000Z
UID:TALK43243@talks.cam.ac.uk
CONTACT:Prof. Neshan Wickramasekera
DESCRIPTION:Let M be a compact manifold. A Ricci-flat metric on M is a\nRi
 emannian metric with vanishing Ricci curvature. Ricci-flat metrics\nare fa
 irly hard to construct\, and their properties are of great interest.\nThey
  are the critical points of the Einstein-Hilbert functional\, the fixed\np
 oints of Hamilton's Ricci flow and the critical points of Perelman's\nlamb
 da-functional.\n\nIn this talk\, we are concerned with the stability prope
 rties of Ricci-flat\nmetrics under Ricci flow. We will prove the following
  stability and\ninstability results. If a Ricci-flat metric is a local max
 imizer of lambda\,\nthen every Ricci flow starting close to it exists for 
 all times and\nconverges (modulo diffeomorphisms) to a nearby Ricci-flat m
 etric. If\na Ricci-flat metric is not a local maximizer of lambda\, then t
 here\nexists a nontrivial ancient Ricci flow emerging from it. This is joi
 nt\nwork with Robert Haslhofer.\n
LOCATION:CMS\, MR11
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