June 19, 2024Open Access

Stability of extremal domains for the first eigenvalue of the Laplacian operator

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Abstract

In this paper, we compute the second variation of the first Dirichlet eigenvalue on extremal domains and establish criteria for stability. We classify the stable extremal domains in the 2-sphere and in higher-dimensional spheres when the boundary is minimal. We also prove topological bounds for stable domains with nonnegative total Gaussian curvature in a general compact Riemannian surface.

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Cavalcante et al. (Wed,) studied this question.

synapsesocial.com/papers/68e642a2b6db6435875d4695 https://doi.org/https://doi.org/10.48550/arxiv.2406.13628

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