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arXiv · 2112.08962

The VMO-Teichm\"uller space and the variant of Beurling-Ahlfors extension by heat kernel

Huaying Wei·Katsuhiko Matsuzaki
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Abstract

We give a real-analytic section for the Teichm\"uller projection onto the VMO-Teichm\"uller space by using the variant of Beurling-Ahlfors extension by heat kernel introduced by Fefferman, Kenig and Pipher in 1991. Based on this result, we prove that the VMO-Teichm\"uller space can be endowed with a real Banach manifold structure that is real-analytically equivalent to its complex Banach manifold structure. We also obtain that the VMO-Teichm\"uller space admits a real-analytic contraction mapping.

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Huaying Wei, Katsuhiko Matsuzaki. 2021-12-16. The VMO-Teichm\"uller space and the variant of Beurling-Ahlfors extension by heat kernel. https://arxiv.org/abs/2112.08962

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