József Lőrinczi: A Faber-Krahn inequality for a class of singular integral operators in bounded domains

Isoperimetric inequalities are of fundamental interest in spectral geometry, and have been studied to a great detail for the Laplacian and related differential operators. In this talk we consider a class of singular integral operators in convex bounded domains subject to Dirichlet exterior conditions, and will be interested in the location of global extrema of the Dirichlet eigenfunctions. As a corollary we will obtain a Faber-Krahn inequality, i.e., that among all convex domains of a fixed volume the lowest Dirichlet eigenvalue is minimised by a ball.