### Abstract

Among all triangles of given diameter, the equilateral triangle is shown to minimize the sum of the first n eigenvalues of the Dirichlet Laplacian, for each n ≥ 1. In addition, the first, second and third eigenvalues are each proved to be minimal for the equilateral triangle. The disk is conjectured to be the minimizer among general domains.

Original language | English (US) |
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Pages (from-to) | 855-885 |

Number of pages | 31 |

Journal | Communications in Analysis and Geometry |

Volume | 19 |

Issue number | 5 |

State | Published - Dec 1 2011 |

### ASJC Scopus subject areas

- Analysis
- Statistics and Probability
- Geometry and Topology
- Statistics, Probability and Uncertainty

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## Cite this

Laugesen, R. S., & Siudeja, B. A. (2011). Dirichlet eigenvalue sums on triangles are minimal for equilaterals.

*Communications in Analysis and Geometry*,*19*(5), 855-885.