Critical Tori for Mean Curvature Energies in Killing Submersions

Alvaro Pampano

doi:10.1016/j.na.2020.112092

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arXiv · 2109.10315

Critical Tori for Mean Curvature Energies in Killing Submersions

Alvaro Pampano

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Abstract

We study surface energies depending on the mean curvature in total spaces of Killing submersions, which extend the classical notion of Willmore energy. Based on a symmetry reduction procedure, we construct vertical tori critical for these mean curvature energies. These vertical tori are based on closed curves critical for curvature energy functionals in Riemannian 2-space forms. The binormal evolution of these critical curves in Riemannian 3-space forms generates rotational tori solutions for an ample family of Weingarten surfaces. Therefore, we also introduce some correspondence results between these two types of tori and illustrate their relation.

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Alvaro Pampano. 2021-09-21. Critical Tori for Mean Curvature Energies in Killing Submersions. https://doi.org/10.1016/j.na.2020.112092

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