##### Department of Mathematics,

University of California San Diego

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### Analysis Seminar

## Nordine Mir

#### Texas A&M University at Qatar

## Regularity of CR maps in positive codimension

##### Abstract:

I will discuss recent joint results with B. Lamel addressing the $C^\infty$ regularity problem for CR mappings between smooth CR submanifolds in complex spaces of possibly different dimension. We essentially show that a nowhere smooth CR map must have its image contained in the set of Dâ€™Angelo infinite type points of the target manifold, from which we derive a number of new regularity results, even in the hypersurface case. Applications to the boundary regularity of proper holomorphic mappings will also be mentioned.

Hosts: Peter Ebenfelt and Ming Xiao

### March 6, 2018

### 1:00 PM

### AP&M 6218

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