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Oct 15, 2015 at 6:10 comment added Julien Bernard Thank you for your anwer. I don't think that the paper answers my conjecture, because it deals with the properties of the geodesic distance at distance, from a point inside a domain and the frontier of the domain. My question is rather linked with the properties of the geodesic distance for infinitesimally close points.
Oct 14, 2015 at 14:31 history answered Igor Rivin CC BY-SA 3.0