Abstract
We investigate geometry of convex domains in a uniformly convex Banach space. We prove that with certain conditions of a metric \(\rho \), \(\rho \)-geodesics are unique, \(\rho \)-geodesics can be prolonged to \(\rho \)-geodesic rays, \(\rho \)-balls are convex. We also show that Ferrand and Kulkarni–Pinkall metrics are examples of such metric.
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Dedicated to David Minda.
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Julian, P.K. On uniqueness and prolongation of geodesics and convexity of balls. J Anal 24, 131–141 (2016). https://doi.org/10.1007/s41478-016-0021-6
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DOI: https://doi.org/10.1007/s41478-016-0021-6