2 problems

Smits's conjecture. If $\Omega$ is a convex bounded domain, then $\Lambda^{\Omega}(\alpha)$ is an increasing function for $\alpha\geq0$. The conjecture concerns monotonicity of the…

Let $V$ be a single-well potential with centered transition point $\tau=0$ or a convex potential, and let $\Lambda(V,\alpha)$ denote the fundamental spectral gap of the one-dimensio…