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math.ST2026
Estimation of Conformal Metrics
Jérôme Taupin
We study deformations of the geodesic distances on a domain of R N induced by a function called conformal factor. We show that under a positive reach assumption on the domain (not…
math.ST2025
Fermat Distance-to-Measure: a robust Fermat-like metric
Jérôme Taupin, Frédéric Chazal
Given a probability measure with density, Fermat distances and density-driven metrics are conformal transformations of the Euclidean metric that shrink distances in high density ar…