Nontrivial minimal surfaces in a hyperbolic Randers space

TL;DR

This paper derives a formula for mean curvature in hyperbolic Randers spaces with Killing fields and constructs explicit examples of nontrivial rotational BH-minimal surfaces, the first of their kind in such spaces.

Contribution

It provides a simple mean curvature formula considering two measures and explicitly constructs the first nontrivial rotational BH-minimal surfaces in hyperbolic Randers spaces.

Findings

Derived a mean curvature formula for hypersurfaces in Randers spaces with Killing fields.

Explicitly constructed the first examples of rotational BH-minimal surfaces in hyperbolic Randers spaces.

Provided local expressions for these minimal surfaces.

Abstract

The contribution of this paper is two-fold. The first one is to derive a simple formula of the mean curvature form for a hypersurface in the Randers space with a Killing field, by considering the Busemann-Hausdorff measure and Holmes-Thompson measure simultaneously. The second one is to obtain the explicit local expressions of two types of nontrivial rotational BH-minimal surfaces in a Randers domain of constant flag curvature $K=-1$, which are the first examples of BH-minimal surfaces in the hyperbolic Randers space.