Almgren's Three-Legged Starfish
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909597083631616 |
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| author | Mantoulidis, Christos Marx-Kuo, Jared |
| author_facet | Mantoulidis, Christos Marx-Kuo, Jared |
| contents | In this note we use classical tools from min-max and hyperbolic geometry to substantiate a folklore example in Almgren--Pitts min-max theory, the three-legged starfish metric on a 2-sphere, whose systolic length, Almgren--Pitts width, and Gromov--Guth width are attained by ``figure-eight'' geodesics. We also recover a hyperbolic geometry fact about ``figure-eight'' geodesics using min-max. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_20895 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Almgren's Three-Legged Starfish Mantoulidis, Christos Marx-Kuo, Jared Differential Geometry In this note we use classical tools from min-max and hyperbolic geometry to substantiate a folklore example in Almgren--Pitts min-max theory, the three-legged starfish metric on a 2-sphere, whose systolic length, Almgren--Pitts width, and Gromov--Guth width are attained by ``figure-eight'' geodesics. We also recover a hyperbolic geometry fact about ``figure-eight'' geodesics using min-max. |
| title | Almgren's Three-Legged Starfish |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2504.20895 |