On left inverses in the Lempert theorem

TL;DR

This paper investigates the existence, uniqueness, and boundary extension of special left inverses called Lempert left inverses in complex geodesics within Lempert domains, focusing on their geometric properties.

Contribution

It provides new insights into the properties and boundary behavior of Lempert left inverses, a specific class of left inverses in complex analysis.

Findings

Characterization of Lempert left inverses via affine hyperplanes

Results on boundary extension and uniqueness of these inverses

Enhanced understanding of complex geodesics in Lempert domains

Abstract

In the paper we discuss the problem of existence, uniqueness and extension through the boundary of left inverses to complex geodesics in Lempert domains. We concentrate on special left inverses (so called Lempert left inverses) characterized by the fact that their fibers are intersections of affine hyperplanes with the domain.