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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.07708 |
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Table of Contents:
- In this article it is shown that the equilateral triangle maximizes the Cheeger constant and minimizes the torsional rigidity among shapes having a fixed minimal width. The proof techniques use direct comparisons with simpler shapes, consisting of disks with three disjoint caps. Comparison results for harmonic functions help establish that in non-equilateral configurations the shape derivative has an appropriate sign, contradicting optimality.