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arXiv · 2609.23484

Embedded constant mean curvature tori in hemispheres of Berger spheres

Jihao Liu·Xiang Ma
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Abstract

We prove that for all real numbers $κ,τ$ with $κ>8τ^2$ and $τ\neq 0$, the Berger sphere $\mathbb{E}^3(κ,τ)$ contains smooth closed embedded rotational surfaces of genus one with constant mean curvature which are contained in an open hemisphere. This disproves a conjecture of Fernández and Mira. The main result of this paper is obtained by generative AI, particularly GPT-5.6-sol, Fable 5, and the Danus system, and then verified by the authors.

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Jihao Liu, Xiang Ma. 2026-09-20. Embedded constant mean curvature tori in hemispheres of Berger spheres. https://arxiv.org/abs/2609.23484

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