Precise estimates of invariant distances on strongly pseudoconvex domains

TL;DR

This paper provides sharp estimates for various invariant distances such as Kobayashi, Lempert, Carathéodory, and Bergman on smooth strongly pseudoconvex domains, enhancing understanding of their geometric behavior.

Contribution

It offers new precise bounds for invariant distances on strongly pseudoconvex domains with specific smoothness conditions, advancing the quantitative analysis of complex geometric structures.

Findings

Sharp estimates for Kobayashi, Lempert, and Carathéodory distances on smooth domains

Precise bounds for Bergman distance on domains with boundary of class C^{3,1}

Improved understanding of geodesic behavior in complex analysis

Abstract

Studying the behavior of real and complex geodesics we provide sharp estimates for the Kobayashi distance, the Lempert function, and the Carath\'eodory distance on $\mathcal{C}^{2,\alpha}$-smooth strongly pseudoconvex domains. Similar estimates are also provided for the Bergman distance on strongly pseudoconvex domains with $\mathcal{C}^{3,1}$-boundary.