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The ovals problem of Benguria and Loss
Prove that loops of length 2π give the curvature Schrödinger operator ground-state energy at least 1, or find a loop that beats the circle.
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| 1 | +{ | |
| 2 | + "domain": "mathematics", | |
| 3 | + "topics": [ | |
| 4 | + "analysis", | |
| 5 | + "mathematical-physics" | |
| 6 | + ], | |
| 7 | + "type": "proof", | |
| 8 | + "also": [ | |
| 9 | + "construction" | |
| 10 | + ], | |
| 11 | + "source": { | |
| 12 | + "key": "alphaevolve", | |
| 13 | + "name": "AlphaEvolve Repository of Problems", | |
| 14 | + "url": "https://google-deepmind.github.io/alphaevolve_repository_of_problems/problems/19.html", | |
| 15 | + "id": "19", | |
| 16 | + "curator": "Google DeepMind", | |
| 17 | + "poser": "Rafael D. Benguria and Michael Loss", | |
| 18 | + "status": "open", | |
| 19 | + "as_of": "2026-10-20", | |
| 20 | + "catalog": "0521c19bbd38" | |
| 21 | + } | |
| 22 | +} | |