Archiv der Mathematik

, Volume 96, Issue 2, pp 187-199

First online:

Krahn’s proof of the Rayleigh conjecture revisited

  • Daniel DanersAffiliated withSchool of Mathematics and Statistics, University of Sydney Email author 

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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.

Mathematics Subject Classification (2010)

35P15 01A60


Rayleigh conjecture Edgar Krahn Faber-Krahn inequality Isoperimetric inequalities Eigenvalue estimates