文摘
The non-uniqueness on geodesics and geodesic disks in the universal asymptotic Teichmüller space AT(D) are studied in this paper. It is proved that if μ is asymptotically extremal in [[μ]] with hζ*(μ) < h*(μ) for some point ζ ∈ ∂D, then there exist infinitely many geodesic segments joining [[0]] and [[μ]], and infinitely many holomorphic geodesic disks containing [[0]] and [[μ]] in AT(D).