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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.
| 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 | } |