2019•Proceedings of the National Academy of SciencesOpen access
Characterizing round spheres using half-geodesics
Ian Adelstein, Benjamin Schmidt
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Abstract
Significance How does one know when a sphere is perfectly round, as opposed to just slightly misshapen? What if this sphere does not live in our usual 3D world, but is instead n -dimensional? We provide geometric conditions sufficient to guarantee that a sphere of arbitrary dimension is round. This question has been widely studied, and our paper adds to the many previous characterizations of round spheres.
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