Entire Constant Mean Curvature Graphs in ${\mathbb{H}}^2\times \mathbb{R}$

Abstract

For $0\le H<1/2$, we construct entire $H$-graphs in ${\mathbb{H}}^2\times \mathbb{R}$ that are parabolic and not invariant by one parameter groups of isometries of ${\mathbb{H}}^2\times \mathbb{R}$. Their asymptotic boundaries are $({\partial }_{\infty }{\mathbb{H}}^2)\times \mathbb{R}$; they are dense at infinity. When $H=0$ the examples are minimal graphs constructed by P. Collin and the second author [2].

References in corpus (2)

• General curvature estimates for stable H-surfaces in 3-manifolds and applications
• Height and area estimates for constant mean curvature graphs in E(κ,τ)-spaces

Cited by in corpus (1)

• Constant mean curvature graphs with prescribed asymptotic values in $\mathbb{E}(-1,\tau )$