The isominwidth problem on the 2-sphere
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910703174025216 |
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| author | Freyer, Ansgar Sagmeister, Ádám |
| author_facet | Freyer, Ansgar Sagmeister, Ádám |
| contents | Pál's isominwidth theorem states that for a fixed minimal width, the regular triangle has minimal area. A spherical version of this theorem was proven by Bezdek and Blekherman, if the minimal width is at most $\tfrac π2$. If the width is greater than $\tfrac π2$, the regular triangle no longer minimizes the area at fixed minimal width. We show that the minimizers are instead given by the polar sets of spherical Reuleaux triangles. Moreover, stability versions of the two spherical inequalities are obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_11462 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The isominwidth problem on the 2-sphere Freyer, Ansgar Sagmeister, Ádám Metric Geometry Pál's isominwidth theorem states that for a fixed minimal width, the regular triangle has minimal area. A spherical version of this theorem was proven by Bezdek and Blekherman, if the minimal width is at most $\tfrac π2$. If the width is greater than $\tfrac π2$, the regular triangle no longer minimizes the area at fixed minimal width. We show that the minimizers are instead given by the polar sets of spherical Reuleaux triangles. Moreover, stability versions of the two spherical inequalities are obtained. |
| title | The isominwidth problem on the 2-sphere |
| topic | Metric Geometry |
| url | https://arxiv.org/abs/2411.11462 |