Tangential Lipschitz Gain and Smoothing Properties of the Bergman Projection
Dr. Sivaguru
TIFR, Mumbai
| Speaker |
Dr. Sivaguru
TIFR, Mumbai
|
|---|---|
| When |
Mar 03, 2017
from 04:00 PM to 05:00 PM |
| Where | LH 006 |
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Abstract: In sharp contrast to $\mathbb{C}$, there is a deep interplay between geometry and the function theory on domains in $\mathbb{C}^n$, $n>1$. We will begin with a quick overview of some of these ideas; focusing, in particular, on pseudoconvexity, finite-type, and circular symmetries. We will then proceed to show that Lipschitz holomorphic functions exhibit a gain in Lipschitz regularity in the complex tangential directions. Finally, we will discuss a smoothing property of the Bergman projection. Along the way, we will highlight connections to the $\overline{\partial}$-Neumann problem and the extension of biholomorphic mappings.