Asymptotic behavior of the Kobayashi metric on convex domains

TL;DR

This paper investigates the asymptotic behavior of the Kobayashi metric on convex domains by estimating invariant metrics using the Sibony metric and exploring potential modifications.

Contribution

It provides new estimates for invariant metrics on convex domains and proposes a possible modification of the Sibony metric.

Findings

Derived estimates for the Sibony metric on convex domains

Analyzed the asymptotic behavior of the Kobayashi metric

Suggested a modification to improve the Sibony metric

Abstract

In this paper, we calculate estimates for invariant metrics on a finite type convex domain in $\mathbb C^n$ using the Sibony metric. We also discuss a possible modification of the Sibony metric.