Stability of extremal domains for the first eigenvalue of the Laplacian operator
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911970737782784 |
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| author | Cavalcante, Marcos P. Nunes, Ivaldo |
| author_facet | Cavalcante, Marcos P. Nunes, Ivaldo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_13628 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stability of extremal domains for the first eigenvalue of the Laplacian operator Cavalcante, Marcos P. Nunes, Ivaldo Differential Geometry Analysis of PDEs 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. |
| title | Stability of extremal domains for the first eigenvalue of the Laplacian operator |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2406.13628 |