The inner radius of nodal domains in high dimensions
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
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| _version_ | 1866917684661190656 |
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| author | Charron, Philippe Mangoubi, Dan |
| author_facet | Charron, Philippe Mangoubi, Dan |
| contents | We prove that every nodal domain of an eigenfunction of the Laplacian of eigenvalue $λ$ on a $d$-dimensional closed Riemannian manifold contains a ball of radius $cλ^{-1/2}(\logλ)^{-(d-2)/2}$. This ball is centered at a point at which the eigenfunction attains its maximum in absolute value within the nodal domain. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_00159 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The inner radius of nodal domains in high dimensions Charron, Philippe Mangoubi, Dan Analysis of PDEs Differential Geometry Spectral Theory We prove that every nodal domain of an eigenfunction of the Laplacian of eigenvalue $λ$ on a $d$-dimensional closed Riemannian manifold contains a ball of radius $cλ^{-1/2}(\logλ)^{-(d-2)/2}$. This ball is centered at a point at which the eigenfunction attains its maximum in absolute value within the nodal domain. |
| title | The inner radius of nodal domains in high dimensions |
| topic | Analysis of PDEs Differential Geometry Spectral Theory |
| url | https://arxiv.org/abs/2306.00159 |