Variance-Refined In-Diameter Lower Bound for the First Dirichlet Eigenvalue

Thomas Schürmann

Let $(M,g)$ be a compact $n$-dimensional Riemannian manifold with nonempty boundary and $n\ge 2$. Assume that $\mathrm{Ric}(M)\ge (n-1)K$ for some $K>0$ and that $\partial M$…