Characterization of Asymptotically Smooth Curves
Complex Variables
2025-10-31 v1
Abstract
We construct an explicit example of an asymptotically conformal chord-arc curve that fails to be asymptotically smooth. This implies that a function belonging to both the little Bloch space and BMOA does not necessarily lie in VMOA, and that a strongly quasisymmetric homeomorphism which is symmetric is not necessarily strongly symmetric. We also provide a complete characterization of asymptotically smooth curves in terms of asymptotic conformality and uniform approximability.
Cite
@article{arxiv.2510.26514,
title = {Characterization of Asymptotically Smooth Curves},
author = {Katsuhiko Matsuzaki and Fei Tao},
journal= {arXiv preprint arXiv:2510.26514},
year = {2025}
}