Non-smooth paths having unit speed with respect to the Kobayashi metric, and their applications
Metric Geometry
2026-01-09 v4 Complex Variables
Abstract
We investigate the question of whether a non-constant absolutely continuous path can be reparametrized to be of unit speed with respect to the Kobayashi metric and be absolutely continuous. Even when the answer is "Yes," which isn't always the case, its proof involves some subtleties. We answer the above question and discuss several applications.
Keywords
Cite
@article{arxiv.2409.03709,
title = {Non-smooth paths having unit speed with respect to the Kobayashi metric, and their applications},
author = {Gautam Bharali and Rumpa Masanta},
journal= {arXiv preprint arXiv:2409.03709},
year = {2026}
}
Comments
17 pages; significant expansion of v3; added a section on applications (Secn. 6) together with two sections dedicated to their proofs (Secns. 7 and 8); provided a more conceptual proof, with fuller details, of Prop. 4.1. This version differs from the final accepted version; the version of record will appear in J. Geom. Anal. Comments still welcome!