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arXiv · 2311.15521

The complex structure of the Teichm\"uller space of circle diffeomorphisms in the Zygmund smooth class

Katsuhiko Matsuzaki
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Abstract

We provide the complex Banach manifold structure for the Teichm\"uller space of circle diffeomorphisms whose derivatives are in the Zygmund class. This is done by showing that the Schwarzian derivative map is a holomorphic split submersion.

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Katsuhiko Matsuzaki. 2023-11-27. The complex structure of the Teichm\"uller space of circle diffeomorphisms in the Zygmund smooth class. https://doi.org/10.1016/j.jmaa.2024.128593

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