15-117 Pavel Exner, Vladimir Lotoreichik

A spectral isoperimetric inequality for cones (878K, Postscript) Dec 9, 15

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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.

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