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SUMMARY:Mean Curvature in the Sphere - Huy Nguyen (Warwick)
DTSTART:20101108T160000Z
DTEND:20101108T170000Z
UID:TALK27740@talks.cam.ac.uk
CONTACT:Prof. Neshan Wickramasekera
DESCRIPTION:One of the broad aims of differential geometry is to classify 
 manifolds with a curvature condition\, a famous example is Hamilton's clas
 sification of three manifolds with positive Ricci curvature\, the seminal 
 result which led to the Ricci flow resolution of Thurston's geometrization
  conjecture. Other results in this vein are the classification of four man
 ifolds with positive isotropic curvature in dimension four by Hamilton\nan
 d two -convex hypersurfaces of Euclidean space of dimension greater than f
 our but Huisken-Sinestrari.\n\nIn this talk\, we will consider the mean cu
 rvature flow in the sphere with a quadratic curvature condition that gener
 alizes the two-convexity condition introduced by Huisken-Sinestrari. We cl
 assify type I solutions and show that the class of such submanifolds is cl
 osed under connected sum. Finally\, we classify type II singularities usin
 g convexity type estimates for mean\ncurvature flow in the sphere.\n
LOCATION:CMS\, MR5
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