The Christoffel problem in the hyperbolic plane.

The horospherical p -Minkowski problem in hyperbolic space H n + 1 was proposed by Li-Xu in [14]. In particular, when n = 1 , p = − 1 , it is called the Christoffel problem in the hyperbolic plane. The corresponding equation is given by φ (φ θ θ − φ θ 2 2 φ + φ − φ − 1 2) = f (θ) , θ ∈ [ 0 , 2 π). In this paper, we obtain two existence results of solutions to the above equation. [ABSTRACT FROM AUTHOR]