A Payne-Weinberger eigenvalue estimate for wedge domains on spheres
  A Faber-Krahn type argument gives a sharp lower estimate for the first Dirichlet eigenvalue for subdomains of wedge domains in spheres, generalizing the inequality in the plane, found by Payne and Weinberger. An application is an alternative proof to the finiteness of a Brownian motion capture time estimate. 
Jesse Ratzkin and Andrejs Treibergs