On a lower bound of the Kobayashi metric

TL;DR

This paper demonstrates that a previously known lower bound for the Kobayashi metric in convex domains does not extend to non-convex domains in complex n-space.

Contribution

The paper establishes that the lower bound of the Kobayashi metric valid for convex domains fails in non-convex domains, clarifying the limitations of existing bounds.

Findings

Lower bound does not hold for non-convex domains

Convexity is crucial for the lower bound to be valid

Highlights the need for different bounds in non-convex settings

Abstract

It is shown that a lower bound of the Kobayashi metric of convex domains in C^n does not hold for non-convex domains.