Archiv der Mathematik

, Volume 96, Issue 2, pp 187–199

Krahn’s proof of the Rayleigh conjecture revisited


DOI: 10.1007/s00013-010-0218-x

Cite this article as:
Daners, D. Arch. Math. (2011) 96: 187. doi:10.1007/s00013-010-0218-x


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)



Rayleigh conjectureEdgar KrahnFaber-Krahn inequalityIsoperimetric inequalitiesEigenvalue estimates

Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsUniversity of SydneySydneyAustralia