The discrete horospherical $p$-Minkowski problem in hyperbolic space

TL;DR

This paper introduces and solves the discrete horospherical p-Minkowski problem in hyperbolic space for all p, focusing on even measures, extending previous smooth domain results.

Contribution

It extends the horospherical p-Minkowski problem to the discrete case for all p and even measures in hyperbolic space, providing a comprehensive solution.

Findings

Solved the discrete horospherical p-Minkowski problem for all p

Established existence and uniqueness results for even measures

Extended previous smooth domain results to the discrete setting

Abstract

In \cite{LX}, the first author and the third author introduced and studied the horospherical $p$-Minkowski problem for smooth horospherically convex domains in hyperbolic space. In this paper, we introduce and solve the discrete horospherical $p$-Minkowski problem in hyperbolic space for all $p\in(-\infty,+\infty)$ when the given measure is even on the unit sphere.