# Boundary behaviour of the Carath\'eodory and Kobayashi-Eisenman volume elements

## TL;DR

This paper investigates how the Carathéodory and Kobayashi-Eisenman volume elements behave near the boundaries of specific complex domains, providing insights into their boundary limits in convex finite type and Levi corank one domains.

## Contribution

It offers new analysis of boundary limits of these volume elements on particular classes of complex domains, extending understanding of their boundary behaviour.

## Key findings

- Boundary limits characterized for convex finite type domains
- Boundary behaviour analyzed for Levi corank one domains
- Enhanced understanding of volume element boundary behaviour

## Abstract

We study the boundary limits of the Carath\'eodory and Kobayashi-Eisenman volume elements on smoothly bounded convex finite type domains and also on Levi corank one domains.