Examples of entire zero-mean curvature graphs of mixed-type in Lorentz-Minkowski space via Konderak's formulas
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910971211022336 |
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| author | Komatsu, Takeki Umehara, Masaaki |
| author_facet | Komatsu, Takeki Umehara, Masaaki |
| contents | Using Konderak's representation formula, we construct an entire zero-mean curvature graph of mixed-type in Lorentz-Minkowski 3-space over a space-like plane, which does not belong to the class of "Kobayashi surfaces". We also point out the existence of an entire zero-mean curvature graph of mixed-type in Lorentz-Minkowski space over a light-like plane. These examples suggest that entire mixed-type zero-mean curvature graphs contain an unexpectedly large number of interesting examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_21869 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Examples of entire zero-mean curvature graphs of mixed-type in Lorentz-Minkowski space via Konderak's formulas Komatsu, Takeki Umehara, Masaaki Differential Geometry Using Konderak's representation formula, we construct an entire zero-mean curvature graph of mixed-type in Lorentz-Minkowski 3-space over a space-like plane, which does not belong to the class of "Kobayashi surfaces". We also point out the existence of an entire zero-mean curvature graph of mixed-type in Lorentz-Minkowski space over a light-like plane. These examples suggest that entire mixed-type zero-mean curvature graphs contain an unexpectedly large number of interesting examples. |
| title | Examples of entire zero-mean curvature graphs of mixed-type in Lorentz-Minkowski space via Konderak's formulas |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2505.21869 |