# On the continuous extension of Kobayashi isometries

## TL;DR

This paper establishes conditions under which Kobayashi isometries between certain convex domains in complex spaces can be continuously extended to their boundaries, generalizing previous results by Zimmer.

## Contribution

It provides a new sufficient condition for the boundary extension of Kobayashi isometries in convex domains with minimal boundary regularity.

## Key findings

- Kobayashi isometries can be extended continuously under the new condition.
- The result applies to domains with boundaries slightly more regular than .
- Generalizes Zimmer's recent boundary extension theorem.

## Abstract

We provide a sufficient condition for the continuous extension of isometries for the Kobayashi distance between bounded convex domains in complex Euclidean spaces having boundaries that are only slightly more regular than $\mathcal{C}^1$. This is a generalization of a recent result by A. Zimmer.