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arXiv · 1305.5028

Riemannian and Finslerian spheres with fractal cut loci

Jinchi Itoh·Sorin V. Sabau
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Abstract

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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Jinchi Itoh, Sorin V. Sabau. 2013-05-22. Riemannian and Finslerian spheres with fractal cut loci. https://arxiv.org/abs/1305.5028

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