A Priori Log-Concavity Estimates for Dirichlet Eigenfunctions
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916553653485568 |
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| author | Khan, Gabriel Saha, Soumyajit Tuerkoen, Malik |
| author_facet | Khan, Gabriel Saha, Soumyajit Tuerkoen, Malik |
| contents | In this paper, we establish a priori log-concavity estimates for the first Dirichlet eigenfunction of convex domains of a Riemannian manifold. Specifically, we focus on cases where the principal eigenfunction $u$ is assumed to be log-concave and our primary goal is to obtain quantitative estimates for the Hessian of $\log u$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_03504 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Priori Log-Concavity Estimates for Dirichlet Eigenfunctions Khan, Gabriel Saha, Soumyajit Tuerkoen, Malik Analysis of PDEs Differential Geometry 58J50 35B45 35B50 In this paper, we establish a priori log-concavity estimates for the first Dirichlet eigenfunction of convex domains of a Riemannian manifold. Specifically, we focus on cases where the principal eigenfunction $u$ is assumed to be log-concave and our primary goal is to obtain quantitative estimates for the Hessian of $\log u$. |
| title | A Priori Log-Concavity Estimates for Dirichlet Eigenfunctions |
| topic | Analysis of PDEs Differential Geometry 58J50 35B45 35B50 |
| url | https://arxiv.org/abs/2501.03504 |