A surgery result for the spectrum of the Dirichlet Laplacian

Dorin Bucur; Dario Mazzoleni

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arXiv · 1410.5179

A surgery result for the spectrum of the Dirichlet Laplacian

Dorin Bucur·Dario Mazzoleni

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Abstract

In this paper we give a method to geometrically modify an open set such that the first $k$ eigenvalues of the Dirichlet Laplacian and its perimeter are not increasing, its measure remains constant, and both perimeter and diameter decrease below a certain threshold. The key point of the analysis relies on the properties of the shape subsolutions for the torsion energy.

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Dorin Bucur, Dario Mazzoleni. 2014-10-20. A surgery result for the spectrum of the Dirichlet Laplacian. https://arxiv.org/abs/1410.5179

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