On minimizing surfaces of the CR invariant energy $E_1$
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918151466254336 |
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| author | Cheng, Jih-Hsin Chiu, Hung-Lin Yang, Paul Zhang, Yongbing |
| author_facet | Cheng, Jih-Hsin Chiu, Hung-Lin Yang, Paul Zhang, Yongbing |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_25780 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On minimizing surfaces of the CR invariant energy $E_1$ Cheng, Jih-Hsin Chiu, Hung-Lin Yang, Paul Zhang, Yongbing Differential Geometry 32V05, 53C45, 53C17 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. |
| title | On minimizing surfaces of the CR invariant energy $E_1$ |
| topic | Differential Geometry 32V05, 53C45, 53C17 |
| url | https://arxiv.org/abs/2509.25780 |