Precise estimates for certain distances in $\mathbb{R}^d$
Differential Geometry
2026-02-17 v1 Complex Variables
Metric Geometry
Abstract
We provide sharp estimates for the intrinsic distances of Finsler metrics with precise boundary estimates. These metrics include the Kobayashi-Hilbert metric near strongly convex points, the minimal metric near convex and strongly minimally convex points, and the -quasi hyperbolic metric in -strongly convex domains. Finally, we prove a characterization result in convex geometry for the -quasi hyperbolic metric.
Keywords
Cite
@article{arxiv.2412.10012,
title = {Precise estimates for certain distances in $\mathbb{R}^d$},
author = {Matteo Fiacchi and Nikolai Nikolov},
journal= {arXiv preprint arXiv:2412.10012},
year = {2026}
}