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arXiv · 1702.05172

Long geodesics on convex surfaces

Arseniy Akopyan·Anton Petrunin
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Abstract

We review the theory of intrinsic geometry of convex surfaces in the Euclidean space and prove the following theorem: if the surface of a convex body K contains arbitrary long closed simple geodesics, then K is an isosceles tetrahedron.

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Arseniy Akopyan, Anton Petrunin. 2017-02-16. Long geodesics on convex surfaces. https://doi.org/10.1007/s00283-018-9795-5

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