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Pré-Publication, Document De Travail Année : 2012

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

Résumé

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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Dates et versions

hal-00676084 , version 1 (02-03-2012)
hal-00676084 , version 2 (23-10-2012)
hal-00676084 , version 3 (18-07-2013)

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Sébastien Cartier, Laurent Hauswirth. Deformations of constant mean curvature 1/2 surfaces in H2xR with vertical ends at infinity. 2012. ⟨hal-00676084v2⟩
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