Title: Monge-Ampère Manifolds: rigidity vs. deformability
Speaker: Giorgio Patrizio
Speaker Info: University of Florence
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Abstract:
I will consider complex manifolds equipped with a plurisubharmonic exhaustion satisfying the top dimensional complex degenerate Monge-Ampère equation outside its minimal set. The minimal set is always small, and in the usual examples it is either a complex submanifold (Stoll's parabolic manifolds) or a maximal dimensional totally real submanifold (Grauert Tubes). The different nature of the minimal set largely determines properties of the ambient manifold, as rigidity properties and deformability features. This, in turn, has consequences in classification and/or characterization results. After a discussion of these aspects, I will outline a class of examples arising in the theory of almost homogeneous manifolds which naturally includes classical examples along with new ones with minimal set of "mixed nature".Date: Saturday, February 21, 2015