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arXiv · 1811.08285

On Conformal Spectral Gap Estimates of the Dirichlet-Laplacian

V. Gol'dshtein·V. Pchelintsev·A. Ukhlov
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Abstract

We study spectral stability estimates of the Dirichlet eigenvalues of the Laplacian in non-convex domains $\Omega\subset\mathbb R^2$. With the help of these estimates we obtain asymptotically sharp inequalities of ratios of eigenvalues in the frameworks of the Payne-P\'olya-Weinberger inequalities. These estimates are equivalent to spectral gap estimates of the Dirichlet eigenvalues of the Laplacian in non-convex domains in terms of conformal (hyperbolic) geometry.

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V. Gol'dshtein, V. Pchelintsev, A. Ukhlov. 2018-11-20. On Conformal Spectral Gap Estimates of the Dirichlet-Laplacian. https://arxiv.org/abs/1811.08285

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