Kobayashi, Carath\'eodory, and Sibony metric

TL;DR

This paper investigates the boundary behavior of the Sibony metric near pseudoconcave points, revealing it diverges at a different rate compared to the Kobayashi metric, thus enhancing understanding of complex geometric metrics.

Contribution

It provides new estimates for the Sibony metric's boundary behavior and compares its divergence rate to the Kobayashi metric near pseudoconcave boundary points.

Findings

Sibony metric blows up near pseudoconcave boundary points

The divergence rate of the Sibony metric differs from the Kobayashi metric

Provides boundary estimates for complex geometric metrics

Abstract

In this paper, we estimate the boundary behavior of the Sibony metric near a pseudoconcave boundary point. We show that the metric blows up at a different rate than the Kobayashi metric.