AlphaEvolve problems·alphaevolve:19
The Ovals Problem
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Let $C$ denote the infimal value of $\\lambda_0(\\gamma)$, the least eigenvalue of the Schrödinger operator $$ H_\\gamma = -\\frac{d^2}{ds^2} + \\kappa^2(s) $$ associated with a simple closed convex curve $\\gamma$ parameterized by arclength and normalized to have length $2\\pi$, where $\\kappa(s)$ is the curvature. Obtain upper and lower bounds for $C$ that are as strong as possible.
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