Minimal hypertori in the four-dimensional sphere
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2021-09-24
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Working Paper
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yes
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Abstract
We prove that the four-dimensional round sphere contains a minimally embedded hypertorus, as well as infinitely many, pairwise non-isometric, immersed ones. Our analysis also yields infinitely many, pairwise non-isometric, minimally embedded hyperspheres and thus provides a self-contained solution to Chern's spherical Bernstein conjecture in dimensions four and six.
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published
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2109.11768
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Cornell University
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09582 - Carlotto, Alessandro (ehemalig) / Carlotto, Alessandro (former)
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947923 - CHallenges in ANalysis and GEometry, between mean and scalar curvature (EC)