, Volume 96, Issue 2, pp 187-199
Date: 22 Jan 2011

Krahn’s proof of the Rayleigh conjecture revisited

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Abstract

The paper is a discussion of Krahn’s proof of the Rayleigh conjecture that amongst all membranes of the same area and the same physical properties, the circular one has the lowest ground frequency. We show how his approach coincides with the modern techniques of geometric measure theory using the co-area formula. We furthermore discuss some issues and generalisations of his proof.