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arXiv 2001.114722020-01math.MGmath.DG

Circumcenter extension maps for non-positively curved spaces

Merlin Incerti-Medici

备注：: V2: Correction of a factor 2 in Theorem D. Comments welcome. 54 pages, 6 figures

英文摘要：

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.

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