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math.MG2020
Circumcenter extension maps for non-positively curved spaces
Merlin Incerti-Medici
We show that every cross ratio preserving homeomorphism between boundaries of Hadamard manifolds extends to a continuous map, called circumcenter extension, provided that the manif…
math.MG2017
The Hausdorff- and Nagata-dimension of Möbius spaces
Merlin Incerti-Medici
We study cross ratios from an axiomatic viewpoint and show that a space equipped with a cross ratios carries several notions of dimension. Specifically, we introduce notions of Hau…
math.MG2017
Möbius structures, quasi-metrics, and completeness
Merlin Incerti-Medici
We study cross ratios from an axiomatic viewpoint, also known as the study of Möbius spaces. We characterise cross ratios induced by quasi-metrics in terms of topological propertie…