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.
Minimal hypertori in the four-dimensional sphere / Carlotto, Alessandro; Schulz, Mario B.. - In: ARS INVENIENDI ANALYTICA.. - ISSN 2769-8505. - 2023, 8:(2023), pp. 1-33. [10.15781/gtrt-v523]
Minimal hypertori in the four-dimensional sphere
Carlotto, Alessandro;
2023-01-01
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.File in questo prodotto:
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