Blow-ups of minimal surfaces in the Heisenberg group
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914861229801472 |
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| author | Yu, Yonghao |
| author_facet | Yu, Yonghao |
| contents | In this paper, we revise Monti's results on the blow-ups of H-perimeter minimizing sets in $\mathbb{H}^n$. Monti demonstrated that the Lipschitz approximation of the blow-up, after rescaling by the square root of the excess, converges to a limit function for $n \ge 2$. However, the partial differential equation he derived for this limit function $φ$ through contact variation is incorrect. Instead, the correct equation is that the horizontal Laplacian of the limit function $φ$ is independent of the coordinate $y_1$ and solves equation 1 weakly. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_05513 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Blow-ups of minimal surfaces in the Heisenberg group Yu, Yonghao Differential Geometry In this paper, we revise Monti's results on the blow-ups of H-perimeter minimizing sets in $\mathbb{H}^n$. Monti demonstrated that the Lipschitz approximation of the blow-up, after rescaling by the square root of the excess, converges to a limit function for $n \ge 2$. However, the partial differential equation he derived for this limit function $φ$ through contact variation is incorrect. Instead, the correct equation is that the horizontal Laplacian of the limit function $φ$ is independent of the coordinate $y_1$ and solves equation 1 weakly. |
| title | Blow-ups of minimal surfaces in the Heisenberg group |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2407.05513 |