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) |
|---|---|
| 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.