Maximizing Neumann fundamental tones of triangles

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 proved for the harmonic and arithmetic means of the first two nonzero eigenvalues.

References in corpus (1)

• Isoperimetric inequalities for eigenvalues of triangles

Cited by in corpus (12)

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• Sums of Laplace eigenvalues - rotationally symmetric maximizers in the plane
• Comparison of the first positive Neumann eigenvalues for rectangles and special parallelograms
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