Maxfaces with infinitely many Swallowtails
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910146328788992 |
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| author | Dhochak, Anu |
| author_facet | Dhochak, Anu |
| contents | In this article, we discuss the existence of a 1-parameter infinite genus family of maxfaces having infinitely many planar (spacelike) ends and infinitely many swallowtails. In particular, we show the existence of the following: (1) a period-2 family of maxfaces with infinitely many planar ends and alternating singularity types, where every odd-layer neck has exactly four swallowtails, while each even-layer neck is almost conical; for $n=2$, the fundamental piece is a genus-1 Wei-type maxface; (2) a period-3 family where every neck carries four swallowtails (24 per period); and (3) a period-2 family of maxfaces with an almost conical singularity on every neck. All maxfaces are embedded in a wider sense. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_17520 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Maxfaces with infinitely many Swallowtails Dhochak, Anu Differential Geometry In this article, we discuss the existence of a 1-parameter infinite genus family of maxfaces having infinitely many planar (spacelike) ends and infinitely many swallowtails. In particular, we show the existence of the following: (1) a period-2 family of maxfaces with infinitely many planar ends and alternating singularity types, where every odd-layer neck has exactly four swallowtails, while each even-layer neck is almost conical; for $n=2$, the fundamental piece is a genus-1 Wei-type maxface; (2) a period-3 family where every neck carries four swallowtails (24 per period); and (3) a period-2 family of maxfaces with an almost conical singularity on every neck. All maxfaces are embedded in a wider sense. |
| title | Maxfaces with infinitely many Swallowtails |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2604.17520 |