Non-holomorphic projections and extension of biholomorphic mappings

TL;DR

This paper demonstrates that biholomorphic mappings between certain smooth, pseudoconvex domains extend smoothly to their boundaries, under a regularity condition on twisted Bergman-like projections, generalizing previous results.

Contribution

It introduces a new sufficient condition involving twisted Bergman-like projections for the smooth extension of biholomorphic maps, broadening the scope of earlier theorems.

Findings

Biholomorphic maps extend smoothly under the new regularity condition.

The regularity condition generalizes Bell and Ligocka's criterion.

The approach involves non-holomorphic projections and boundary regularity analysis.

Abstract

We show that biholomorphic mappings between two bounded, pseudoconvex domains with smooth boundary extend smoothly to the boundaries of the domains, under a regularity condition on a family of twisted Bergman-like projections. This result is inspired by and generalizes a sufficient condition for extension due to Bell and Ligocka.