Archiv der Mathematik

, Volume 96, Issue 2, pp 187–199

Krahn’s proof of the Rayleigh conjecture revisited

Authors

    • School of Mathematics and StatisticsUniversity of Sydney
Article

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

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.

Mathematics Subject Classification (2010)

35P1501A60

Keywords

Rayleigh conjectureEdgar KrahnFaber-Krahn inequalityIsoperimetric inequalitiesEigenvalue estimates

Copyright information

© Springer Basel AG 2011