%0 Journal Article
%T A spectral isoperimetric inequality for cones
%A Pavel Exner
%A Vladimir Lotoreichik
%J Mathematics
%D 2015
%I arXiv
%X In this note we investigate three-dimensional Schr\"odinger operators with $\delta$-interactions supported on $C^2$-smooth cones, both finite and infinite. Our main results concern a Faber-Krahn-type inequality for the principal eigenvalue of these operators. The proofs rely on the Birman-Schwinger principle and on the fact that circles are unique minimisers for a class of energy functionals.
%U http://arxiv.org/abs/1512.01970v1