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math.MG2021
The Four Point Condition: An Elementary Tropicalization of Ptolemy's Inequality
Mario Gómez, Facundo Mémoli
Ptolemy's inequality is a classic relationship between the distances among four points in Euclidean space. Another relationship between six distances is the 4-point condition, an i…
math.AT2021
Curvature Sets Over Persistence Diagrams
Mario Gómez, Facundo Mémoli
We study a family of invariants of compact metric spaces that combines the Curvature Sets defined by Gromov in the 1980s with Vietoris-Rips Persistent Homology. For given integers…