On minimizing surfaces of the CR invariant energy $E_1$

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

On minimizing surfaces of the CR invariant energy $E_1$

Differential Geometry 2025-10-01 v1

Authors: Jih-Hsin Cheng , Hung-Lin Chiu , Paul Yang , Yongbing Zhang

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.

Keywords

CR invariant energy functional Heisenberg group minimal surfaces second variation Clifford torus

Cite

@article{arxiv.2509.25780,
  title  = {On minimizing surfaces of the CR invariant energy $E_1$},
  author = {Jih-Hsin Cheng and Hung-Lin Chiu and Paul Yang and Yongbing Zhang},
  journal= {arXiv preprint arXiv:2509.25780},
  year   = {2025}
}

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28 pages, 3 figures

On minimizing surfaces of the CR invariant energy $E_1$

Abstract

Keywords

Cite

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