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arXiv · 2510.26514

Characterization of Asymptotically Smooth Curves

Katsuhiko Matsuzaki·Fei Tao
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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.

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Katsuhiko Matsuzaki, Fei Tao. 2025-10-30. Characterization of Asymptotically Smooth Curves. https://arxiv.org/abs/2510.26514

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