Maximizing Neumann fundamental tones of triangles

Details Maximizing Neumann fundamental tones of triangles Maximizing Neumann fundamental tones of triangles

2009-07-09

arxiv.org/abs/0907.1562v1

Mathematics

Spectral Theory

Scientific paper

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.

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