On minimizing surfaces of the CR invariant energy $E_1$

Jih-Hsin Cheng; Hung-Lin Chiu; Paul Yang; Yongbing Zhang

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arXiv · 2509.25780

On minimizing surfaces of the CR invariant energy $E_1$

Jih-Hsin Cheng·Hung-Lin Chiu·Paul Yang·Yongbing Zhang

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Abstract

We study a CR-invariant equation for vanishing $E_1$ surfaces in the 3-dimensional Heisenberg group. This is shown to be a hyperbolic equation. We prove the local uniqueness theorem for an initial value problem and classify all such global surfaces with rotational symmetry. We also show that the Clifford torus in the CR 3-sphere is not a local minimizer of $E_1$ by computing the second variation.

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BibTeX RIS

Jih-Hsin Cheng, Hung-Lin Chiu, Paul Yang, Yongbing Zhang. 2025-09-30. On minimizing surfaces of the CR invariant energy $E_1$. https://arxiv.org/abs/2509.25780

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