Extremal and stationary discs for the Kobayashi $k$-metric

TL;DR

This paper extends the theory of extremal and stationary discs for the Kobayashi metric to higher order cases, broadening the understanding of complex geometric structures.

Contribution

It generalizes existing results on extremal discs for the Kobayashi metric to a higher order setting, providing new insights into complex geometry.

Findings

Extended the description of extremal discs to higher order Kobayashi metrics

Connected extremal discs with stationary discs in the higher order context

Provided a framework for analyzing complex geometric structures using higher order extremal discs

Abstract

We generalize Lempert's and Poletsky's works on the description of extremal discs for the Kobayashi metric to a higher order setting.