### Abstract

We prove sharp isoperimetric inequalities for Neumann eigenvalues of the Laplacian on triangular domains. The first nonzero Neumann eigenvalue is shown to be maximal for the equilateral triangle among all triangles of given perimeter, and hence among all triangles of given area. Similar results are proven for the harmonic and arithmetic means of the first two nonzero eigenvalues.

Original language | English (US) |
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Article number | 112903 |

Journal | Journal of Mathematical Physics |

Volume | 50 |

Issue number | 11 |

DOIs | |

State | Published - Dec 24 2009 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Laugesen, R. S., & Siudeja, B. A. (2009). Maximizing Neumann fundamental tones of triangles.

*Journal of Mathematical Physics*,*50*(11), [112903]. https://doi.org/10.1063/1.3246834