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arXiv · 1512.01970

A spectral isoperimetric inequality for cones

Pavel Exner·Vladimir Lotoreichik
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Abstract

In this note we investigate three-dimensional Schrödinger operators with $δ$-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 minimizers for a class of energy functionals. The main novel idea consists in the way of constructing test functions for the Birman-Schwinger principle.

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Pavel Exner, Vladimir Lotoreichik. 2016-11-01. A spectral isoperimetric inequality for cones. https://doi.org/10.1007/s11005-016-0917-8

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