Bounds for exit times of Brownian motion and the first Dirichlet eigenvalue for the Laplacian

Rodrigo Banuelos, Phanuel Mariano, Jing Wang

For domains in ${\mathbb{R}}^d$, $d\ge 2$, we prove universal upper and lower bounds on the product of the bottom of the spectrum for the Laplacian to the power $p>0$ and the suprem…