Uniqueness of the Faber–Krahn Position of Convex Bodies
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Statement
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.
Context
Answers a 2011 question and yields a new proof of the Pólya–Szegő theorem for triangles as a consequence.
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