Uniqueness of the Faber–Krahn Position of Convex Bodies
A convex body is in Faber-Krahn position if it minimizes the first Dirichlet eigenvalue within its volume-preserving linear orbit. The paper proves this position is unique up to orthogonal transformations, answering a question of Schmuckenschläger from 2011, via a new log-convexity property of the first eigenvalue under positive definite linear deformations.
- Result
- Proved
- Status
- Resolved
- AI contribution
- AI-assisted
- Method
- Argument
- Field
- Spectral Geometry, Convex Geometry
- Posed by
- Michael Schmuckenschläger
- Year posed
- 2011
- Years open
- 15y
- Solved
- 2026-07-23
- Model
- ChatGPT
- Vendor
- OpenAI
- Collaborators
- Dmitry Faifman, Iosif Polterovich
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 20 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The AI usage disclosure says only that the authors made use of ChatGPT for mathematical discussions and editorial assistance. It does not separate the two, so the lowest tier applies.
Verification
No independent check, and the disclosure is general rather than pointing at any specific result. Preprint, not refereed.