Constant mean curvature graphs in a class of warped product spaces

Abstract

We introduce a new existence result for compact normal geodesic graphs with constant mean curvature and boundary in a class of warped product spaces. In particular, our result includes that of normal geodesic graphs with constant mean curvature in hyperbolic space \({\mathbb{H}^{n+1}}\) over a bounded domain in a totally geodesic \({\mathbb{H}^{n} \subset \mathbb{H}^{n+1}}\) .