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arXiv · 2204.05736

Quasi-Fuchsian manifolds close to the Fuchsian locus are foliated by constant mean curvature surfaces

Diptaishik Choudhury·Filippo Mazzoli·Andrea Seppi
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Abstract

Even though it is known that there exist quasi-Fuchsian hyperbolic three-manifolds that do not admit any monotone foliation by constant mean curvature (CMC) surfaces, a conjecture due to Thurston asserts the existence of CMC foliations for all almost-Fuchsian manifolds, namely those quasi-Fuchsian manifolds that contain a closed minimal surface with principal curvatures in (-1,1). In this paper we prove that there exists a (unique) monotone CMC foliation for all quasi-Fuchsian manifolds that lie in a sufficiently small neighborhood of the Fuchsian locus.

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Diptaishik Choudhury, Filippo Mazzoli, Andrea Seppi. 2022-04-12. Quasi-Fuchsian manifolds close to the Fuchsian locus are foliated by constant mean curvature surfaces. https://arxiv.org/abs/2204.05736

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