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arXiv · 1705.02951

Embedded $H$-Planes in Hyperbolic 3-Space

Baris Coskunuzer
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Abstract

We show that for any C^0 Jordan curve C in the sphere at infinity of H^3, there exists an embedded $H$-plane P_H in H^3 with asymptotic boundary C for any H in (-1,1). As a corollary, we proved that any quasi-Fuchsian hyperbolic 3-manifold M=SxR contains an H-surface S_H in the homotopy class of the core surface S for any H in (-1,1). We also proved that for any C^1 Jordan curve J in the sphere at infinity, there exists a unique minimizing H-plane P_H with asymptotic boundary J for a generic H in (-1,1).

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Baris Coskunuzer. 2017-05-08. Embedded $H$-Planes in Hyperbolic 3-Space. https://doi.org/10.1090/tran%2F7286

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