Asymptotically hyperbolic manifold with a horospherical boundary

TL;DR

This paper studies a class of asymptotically hyperbolic manifolds with noncompact boundaries resembling horospheres, providing geometric formulas and analyzing their properties in hyperbolic space.

Contribution

It introduces a new class of asymptotically hyperbolic manifolds with horospherical boundaries and derives relevant geometric formulas.

Findings

Characterization of asymptotically hyperbolic manifolds with horospherical boundaries

Derivation of geometric formulas for these manifolds

Analysis of model cases like horoballs in hyperbolic space

Abstract

We discuss asymptotically hyperbolic manifold with a noncompact boundary which is close to a horosphere in a certain sense. The model case is a horoball or the complement of a horoball in standard hyperbolic space. We show some geometric formulas.