Smoothness to the boundary of biholomorphic mappings

TL;DR

This paper demonstrates that under certain geometric conditions, biholomorphic maps between smoothly bounded, pseudoconvex domains can be extended smoothly to their boundaries, ensuring a diffeomorphic boundary correspondence.

Contribution

It establishes boundary regularity extension results for biholomorphic mappings under a new geometric hypothesis.

Findings

Biholomorphic maps extend to boundary as diffeomorphisms

Extension relies on a specific geometric condition

Results apply to smoothly bounded, pseudoconvex domains

Abstract

Under a plausible geometric hypothesis, we show that a biholomorphic mapping of smoothly bounded, pseudoconvex domains extends to a diffeomorphism of the closures.