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CATEGORIES:Geometric Analysis and Partial Differential Equati
ons seminar
SUMMARY:Mean Curvature in the Sphere - Huy Nguyen (Warwick
)
DTSTART;TZID=Europe/London:20101108T160000
DTEND;TZID=Europe/London:20101108T170000
UID:TALK27740AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/27740
DESCRIPTION:One of the broad aims of differential geometry is
to classify manifolds with a curvature condition\,
a famous example is Hamilton's classification of
three manifolds with positive Ricci curvature\, th
e seminal result which led to the Ricci flow resol
ution of Thurston's geometrization conjecture. Oth
er results in this vein are the classification of
four manifolds with positive isotropic curvature i
n dimension four by Hamilton\nand two -convex hype
rsurfaces of Euclidean space of dimension greater
than four but Huisken-Sinestrari.\n\nIn this talk\
, we will consider the mean curvature flow in the
sphere with a quadratic curvature condition that g
eneralizes the two-convexity condition introduced
by Huisken-Sinestrari. We classify type I solution
s and show that the class of such submanifolds is
closed under connected sum. Finally\, we classify
type II singularities using convexity type estimat
es for mean\ncurvature flow in the sphere.\n
LOCATION:CMS\, MR5
CONTACT:Prof. Neshan Wickramasekera
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