A sharp relative isoperimetric inequality for the square
We compute the exact value of the least “relative perimeter” of a shape $S$, with a given area, contained in a unit square; the relative perimeter of $S$ being the length of the boundary of $S$ that does not touch the border of the square.
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Académie des sciences
2021-11-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.243/ |
| Summary: | We compute the exact value of the least “relative perimeter” of a shape $S$, with a given area, contained in a unit square; the relative perimeter of $S$ being the length of the boundary of $S$ that does not touch the border of the square. |
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| ISSN: | 1778-3569 |