Asymptotically Hyperbolic Manifolds with Boundary Conjugate Points but no Interior Conjugate Points

TL;DR

This paper constructs specific asymptotically hyperbolic manifolds that have boundary conjugate points while lacking interior conjugate points, challenging previous assumptions about their geometric properties.

Contribution

It introduces a novel class of non-trapping asymptotically hyperbolic manifolds with boundary conjugate points but no interior conjugate points, expanding understanding of their geometric structure.

Findings

Existence of such manifolds disproves previous conjectures

Provides explicit construction methods for these manifolds

Highlights differences between boundary and interior conjugate points

Abstract

We construct non-trapping asymptotically hyperbolic manifolds with boundary conjugate points but no interior conjugate points.