Kobayashi-Royden pseudometric vs. Lempert function

TL;DR

This paper demonstrates that in non-taut domains, the Kobayashi-Royden pseudometric does not always correspond to the derivative of the Lempert function, challenging assumptions about their relationship.

Contribution

It provides a specific example illustrating the disconnect between the Kobayashi-Royden pseudometric and the Lempert function in certain complex domains.

Findings

Kobayashi-Royden pseudometric is not always the derivative of the Lempert function in non-taut domains.

The paper clarifies the limitations of the relationship between these two complex geometric tools.

It highlights the need for careful analysis when applying these metrics to non-taut domains.

Abstract

We give an example showing that the Kobayashi-Royden pseudometric for a non-taut domain is, in general, not the derivative of the Lempert function.