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SUMMARY:Sasaki geometry and positive curvature - Song Sun (Imperial Colleg
 e)
DTSTART:20120413T093000Z
DTEND:20120413T103000Z
UID:TALK36843@talks.cam.ac.uk
CONTACT:Dr. J Ross
DESCRIPTION:We classify simply connected compact Sasaki manifolds with pos
 itive transverse bisectional curvature. In particular\, the moduli space o
 f all such manifolds can be contracted to a point-- the standard round sph
 ere. This provides an alternative proof of  the Mori-Siu-Yau theorem on Fr
 ankel conjecture as well as extends it to the orbifold case. \n\nThe proof
  involves deforming any such manifold towards the round sphere\, through a
 n infinite dimensional evolution equation followed by a finite dimensional
  ``volume decreasing flow". The latter can only be done within the framewo
 rk of Sasaki geometry and is inspired by the work of Martelli-Sparks-Yau o
 n volume minimization. Time permitting we will also talk about the case wh
 en the  positivity assumption is replaced by non-negativity. This talk is 
 based on joint work with Weiyong He. 
LOCATION:MR2
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