Sharp bounds for eigenvalues of triangles

B. Siudeja

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arXiv · math/0603630

Sharp bounds for eigenvalues of triangles

B. Siudeja

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Abstract

We prove that the first eigenvalue of the Dirichlet Laplacian for a triangle in the plane is bounded above by $π^2 L^2\over 9A^2$, where $L$ is the perimeter and $A$ is the area of this triangle. We show that the \mbox{constant 9} is optimal and that the optimal constant for the lower bound of the same form is 16. This gives a positive answer to a conjecture made by P. Freitas.

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BibTeX RIS

B. Siudeja. 2006-03-27. Sharp bounds for eigenvalues of triangles. https://arxiv.org/abs/math/0603630

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