Total curvature of a complete minimal surface and the modified defect relation of a Fermat hypersurface for the Gauss map
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866916049904992256 |
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| author | Quang, Si Duc Chi, Nguyen Thi Quynh |
| author_facet | Quang, Si Duc Chi, Nguyen Thi Quynh |
| contents | In this paper, we establish some modified defect relations for the Gauss map $g$ of a complete minimal surface $S\subset\mathbb R^m$ into $\mathbb P^n(\mathbb C)\ (n=m-1)$ with only a single Fermat hypersurface $Q$ of $\mathbb P^n(\mathbb C)$. In particular, we show that $S$ must have finite total curvature if the image $g(S)$ intersects $Q$ with only a finite number of times and the degree of $Q$ is sufficiently large. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_27001 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Total curvature of a complete minimal surface and the modified defect relation of a Fermat hypersurface for the Gauss map Quang, Si Duc Chi, Nguyen Thi Quynh Differential Geometry In this paper, we establish some modified defect relations for the Gauss map $g$ of a complete minimal surface $S\subset\mathbb R^m$ into $\mathbb P^n(\mathbb C)\ (n=m-1)$ with only a single Fermat hypersurface $Q$ of $\mathbb P^n(\mathbb C)$. In particular, we show that $S$ must have finite total curvature if the image $g(S)$ intersects $Q$ with only a finite number of times and the degree of $Q$ is sufficiently large. |
| title | Total curvature of a complete minimal surface and the modified defect relation of a Fermat hypersurface for the Gauss map |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2605.27001 |