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Stephen S-T. Yau

2011-08-10
15:00:00 - 16:00:00

308 , Mathematics Research Center Building (ori. New Math. Bldg.)

We shall discuss rigidity phenomenon of CR morphisms between compact strongly pseudoconvex CR manifolds. In particular, we shall prove the following result. Let X_1, X_2 be two 3-dimensional compact strongly pseudoconvex CR manifolds sitting inside a 2-dimensional variety V with only isolated singularities in C^n. Let V_1, V_2 be two varieties in V such that their boundaries are X_1, X_2 respectively. Suppose that V, V_1, V_2 have the same singular set. Then nontrivial CR morphism from X_1 to X_2 are CR biholomorphisms.

As a corollary, we have proven the following Theorem. Let X be a 3-dimensional compact strongly pseudoconvex CR manifolds sitting inside C^n. Then nontrivial CR morphisms from X to itself are automorphisms.