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arXiv · 1203.0760

Deformations of constant mean curvature 1/2 surfaces in H2xR with vertical ends at infinity

Sébastien Cartier·Laurent Hauswirth
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Abstract

We study constant mean curvature 1/2 surfaces in H2xR that admit a compactification of the mean curvature operator. We show that a particular family of complete entire graphs over H2 admits a structure of infinite dimensional manifold with local control on the behaviors at infinity. These graphs also appear to have a half-space property and we deduce a uniqueness result at infinity. Deforming non degenerate constant mean curvature 1/2 annuli, we provide a large class of (non rotational) examples and construct (possibly embedded) annuli without axis, i.e. with two vertical, asymptotically rotational, non aligned ends.

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Sébastien Cartier, Laurent Hauswirth. 2013-07-19. Deformations of constant mean curvature 1/2 surfaces in H2xR with vertical ends at infinity. https://doi.org/10.4310/cag.2014.v22.n1.a2

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