##### Department of Mathematics,

University of California San Diego

****************************

### Math 248 - Analysis

## J.M. Lee

#### University of Washington

## Foliations of CR manifolds and estimates for tangential Cauchy-Riemann

##### Abstract:

The $overlinepartial_b$-Neumann problem is the analog for CR manifolds of the $overlinepartial$-Neumann problem. All positive results about this problem so far have applied to domains with a defining function depending only on the real and imaginary parts of a single CR function. The key feature of such domains is that they are foliated (away from a characteristic curve) by compact, strictly pseudoconvex CR submanifolds of real codimension 2. I will describe a new approach to finding estimates based on decomposing the operator into its tangential and transverse parts with respect to this foliation. Estimates for the tangential parts follow from known results about the tangential Cauchy-Riemann complex on compact CR manifolds, while estimates for the transverse part reduce to elliptic estimates in the plane. For certain domains in the Heisenberg group, my student Robert Hladky has used this method to obtain sharp boundary regularity, even near characteristic points.

Host: Peter Ebenfelt

### February 19, 2004

### 10:00 PM

### AP&M 7321

****************************