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arXiv · 2406.13628

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

Marcos P. Cavalcante·Ivaldo Nunes
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Abstract

In this paper, we compute the second variation of the first Dirichlet eigenvalue on extremal domains in general Riemannian manifolds and establish a criterion for stability. We classify the stable extremal domains in the 2-sphere and higher-dimensional spheres when the boundary is minimal. Additionally, we establish topological bounds for stable domains in a general compact Riemannian surface, assuming either nonnegative total Gaussian curvature or small volume.

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Marcos P. Cavalcante, Ivaldo Nunes. 2024-06-19. Stability of extremal domains for the first eigenvalue of the Laplacian operator. https://arxiv.org/abs/2406.13628

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