Abstract
AbstractWe show that every cross ratio preserving homeomorphism between boundaries of Hadamard manifolds extends to a map, called circumcenter extension, provided that the manifolds satisfy certain visibility conditions. We describe regions on which this map is Hölder-continuous. Furthermore, we show that this map is a rough isometry, whenever the manifolds admit cocompact group actions by isometries and we improve previously known quasi-isometry constants, provided by Biswas, in the case of 2-dimensional $$\mathrm {CAT(-1)}$$
CAT
(
-
1
)
manifolds. Finally, we provide a sufficient condition for this map to be an isometry in the case of Hadamard surfaces.
Funder
Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung
FWF Österreichischer Wissenschaftsfond
University of Vienna
Publisher
Springer Science and Business Media LLC