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题目：3维紧强拟凸CR流形之间的CR态射的刚性与奇点解消

Title: Resolution of singularities and rigidity of CR morphisms between 3-dimensional compact strongly pseudoconvex CR manifolds.

报告人：丘成栋教授 （伊利诺伊大学）

时间：2011年5月9日(周一)下午15:00-16:00

地点：闵行校区数学楼102报告厅

Abstract:

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.