Helicoidal minimal surfaces in hyperbolic space

Minimal translation surfaces in hyperbolic space

In the half-space model of hyperbolic space, that is, R+ = {(x, y, z) ∈ R ; z > 0} with the hyperbolic metric, a translation surface is a surface that writes as z = f(x) + g(y) or y = f(x) + g(z), where f and g are smooth functions. We prove that the only minimal translation surfaces (zero mean curvature in all points) are totally geodesic planes. MSC: 53A10

Hermite Polynomials And Helicoidal Minimal Surfaces

The main objective of this paper is to construct smooth 1-parameter families of embedded minimal surfaces in euclidean space that are invariant under a screw motion and are asymptotic to the helicoid. Some of these families are significant because they generalize the screw motion invariant helicoid with handles and thus suggest a pathway to the construction of higher genus helicoids. As a bypro...

On helicoidal ends of minimal surfaces

Linear Weingarten Helicoidal Surfaces in Isotropic Space

Introduced in 1861 [1], a Weingarten surface in the Euclidean three-dimensional space E3 is a surface M, whose mean curvature H and Gaussian curvature K satisfy a non-trivial relation Φ(H, K) = 0. Such a surface was introduced by Weingarten. The class of Weingarten surfaces is remarkably large, and it consists of intriguing surfaces in the Euclidean space: the constant mean curvature surfaces, ...

Eigenvalue estimates for minimal surfaces in hyperbolic space

This paper gives an upper bound for the first eigenvalue of the universal cover of a complete, stable minimal surface in hyperbolic space, and a sharper one for least area disks.