In this talk we will prove a result about the continuous extension of planar biholomorphisms between domains that are not necessarily simply connected and that are allowed to have boundaries that are very rough. The novelty of this work lies in the fact that it uses the so-called visibility property of Kobayashi geodesics (which has been much-studied in recent years) and, more generally, ideas and strategies that are most commonly associated with the study of Gromov hyperbolic distance spaces.
We will provide a quick introduction to the visibility property and to some other topics that are necessary for understanding the statement and proof of the result, and then briefly outline the proof, taking care to point out the insights that underlie key steps in the proof. We will conclude by pointing out possible generalisations. This is joint work with V.S. Chandel, S. Gorai and A.D. Sarkar, and is a generalisation of recent work of a similar nature by G. Bharali and A. Zimmer.
