Riemannian and Finslerian spheres with fractal cut loci
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🧮 math.DG
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fractalriemannianspherebecomescasecertainconstructconstruction
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The present paper shows that for a given integer k greater than 2 it is possible to construct an at least k-differentiable Riemannian metric on the sphere of a certain dimension such that the cut locus of a point of it becomes a fractal. Moreover, we show that this construction can be extended to the case of Finsler sphere as well.
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