When do Fermat constants completely determine Clairaut constants for branching geodesics on a surface of revolution?

2023/07/16 by Anastasios N. Zachos, Zachos, Anastasios N.
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Advanced Differential Equations and Dynamical Systems

paper · pdf · doi:10.48550/arxiv.2310.07717

Abstract

We prove that Fermat constants do not completely determine Clairaut constants for three branching geodesics that meet at the weighted Fermat-Torricelli point on a surface of revolution, except the case of a standard sphere in ℝ³.

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