Strong localizations of the Kobayashi distance
Nikolai Nikolov, Ahmed Yekta \"Okten
TL;DR
This paper establishes new strong localization results for the Kobayashi distance by identifying sufficient growth conditions related to the behavior of Kobayashi geodesics, enhancing understanding of its local properties.
Contribution
It introduces novel growth conditions that lead to strong multiplicative and additive localizations of the Kobayashi distance, connecting these conditions to geodesic behavior.
Findings
New growth conditions for Kobayashi distance localization
Strong multiplicative and additive localization results
Connection between geodesic behavior and localization
Abstract
Recently, the visibility property of Kobayashi (almost) geodesics has been used to provide localizations of the Kobayashi distance. In this note, we provide sufficient growth conditions for the Kobayashi distance to obtain new strong multiplicative and additive localization results. Curiously, the conditions we provide are deeply related to the behaviour of the Kobayashi geodesics.
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Taxonomy
TopicsHolomorphic and Operator Theory · Geometric Analysis and Curvature Flows · Nonlinear Differential Equations Analysis