[CvGmt News] GFO-Pisa Seminars
Carlo Mantegazza
c.mantegazza at sns.it
Thu May 7 13:27:56 CEST 2009
Thursday 7/5/09 - Lorenzo Mazzieri
Title: Connected sum construction for sigma_k-Yamabe metrics.
Abstract: Given two closed n-dimensional Riemannian manifolds
(M_1,g_1) and (M_2,g_2) with positive constant sigma_k-curvature, 1<2k<n,
we construct on the connected sum M_m = (M_1) # (M_2) a family of metrics
{g_m} with positive constant sigma-curvature, the parameter m>0 being
the necksize. Moreover, we have that the new metrics tend to the old ones
on the compact subset of the summands, as m ends to 0.
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Friday 8/5/09 - Charles Baker
Title: Mean curvature flow of submanifolds of high codimension
Abstract: We present results from the speaker's doctoral thesis
concerning the mean curvature flow of submanifolds of arbitrary
codimension of both Euclidean and spherical backgrounds. In particular,
we show that under a certain pinching condition the submanifolds flow to
round points in finite time. These results may be considered as high
codimension analogues of the corresponding hypersurface theorems of Huisken.
Also new is special connection used on the spacetime product manifold
that builds in the Uhlenbeck trick, which simplifies the derivation of
evolution equations of geometric quantities.
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