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

Sébastien Cartier (1) , Laurent Hauswirth (1)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

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.

Mots clés: Constant mean curvature; Vertical ends; Entire graphs; Vertical annuli

Domaines: Géométrie différentielle [math.DG]

Sébastien Cartier, Laurent Hauswirth. Deformations of constant mean curvature 1/2 surfaces in H2xR with vertical ends at infinity. Communications in Analysis and Geometry, 2014, 22 (1), pp.109--148. ⟨10.4310/CAG.2014.v22.n1.a2⟩. ⟨hal-00676084v3⟩