[CvGmt News] GFO-Pisa Seminars

[Carlo Mantegazza]

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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