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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2305.06517 |
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| _version_ | 1866915356389408768 |
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| author | Cui, Hongbin Jiao, Xiaoxiang Xu, Xiaowei |
| author_facet | Cui, Hongbin Jiao, Xiaoxiang Xu, Xiaowei |
| contents | There are two significant families of minimal real matrix varieties: determinantal varieties and skew-symmetric determinantal varieties, the later ones are also known as Pfaffian varieties. In 1999, Kerckhove and Lawlor [Duke Math.J. 96(2),401--424,1999] proved that determinantal varieties are area-minimizing except for two families. In this paper we prove that all Pfaffian varieties are area-minimizing with the exception of Pfaffian hypersurfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_06517 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On area-minimizing Pfaffian varieties Cui, Hongbin Jiao, Xiaoxiang Xu, Xiaowei Algebraic Geometry Differential Geometry Primary 49Q15, 53A10, 53A07, Secondary 14M12, 14M99 There are two significant families of minimal real matrix varieties: determinantal varieties and skew-symmetric determinantal varieties, the later ones are also known as Pfaffian varieties. In 1999, Kerckhove and Lawlor [Duke Math.J. 96(2),401--424,1999] proved that determinantal varieties are area-minimizing except for two families. In this paper we prove that all Pfaffian varieties are area-minimizing with the exception of Pfaffian hypersurfaces. |
| title | On area-minimizing Pfaffian varieties |
| topic | Algebraic Geometry Differential Geometry Primary 49Q15, 53A10, 53A07, Secondary 14M12, 14M99 |
| url | https://arxiv.org/abs/2305.06517 |