Circumcenter extension maps for non-positively curved spaces
Metric Geometry
2022-01-06 v3 Differential Geometry
Abstract
We show that every cross ratio preserving homeomorphism between boundaries of Hadamard manifolds extends to a continuous map, called circumcenter extension, provided that the manifolds satisfy certain visibility conditions. We show that this map is a rough isometry, whenever the manifolds admit cocompact group actions by isometries and we improve the quasi-isometry constants provided by Biswas in the case of CAT(-1)} spaces. Finally, we provide a sufficient condition for this map to be an isometry in the case of Hadamard surfaces.
Cite
@article{arxiv.2001.11472,
title = {Circumcenter extension maps for non-positively curved spaces},
author = {Merlin Incerti-Medici},
journal= {arXiv preprint arXiv:2001.11472},
year = {2022}
}
Comments
V2: Correction of a factor 2 in Theorem D. Comments welcome. 54 pages, 6 figures