Deformations of constant mean curvature-1/2 surfaces in $\mathbb{H}^2 \times \mathbb{R}$ with vertical ends at infinity
Year: 2014
Type: article
Abstract: We study constant mean curvature (CMC)-1/2 surfaces in H 2 × R that admit a compactification of the mean curvature operator.We show that a particular family of complete entire graphs over H 2 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 CMC-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.
Authors: Sébastien Cartier, Laurent Hauswirth
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2166756445