Pavel Exner, Vladimir Lotoreichik
A spectral isoperimetric inequality for cones
(878K, Postscript)

ABSTRACT.  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.