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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.13072 |
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| _version_ | 1866918160875126784 |
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| author | Wei, Guofang Xiao, Ling |
| author_facet | Wei, Guofang Xiao, Ling |
| contents | In this paper, we prove that the first eigenfunction of the Laplacian for a horo-convex domain $Ω\subset\mathbb H^n$ is super log-concave when $\text{diam}(Ω)$ is not large. Our result is optimal in the sense that there are counterexamples %are constructed for the cases when $Ω$ is not horo-convex or when $\text{diam}(Ω)$ is large respectively |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_13072 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Super Log-concavity of the First Eigenfunctions for Horo-convex Domains in Hyperbolic Space Wei, Guofang Xiao, Ling Analysis of PDEs Differential Geometry 58, 35 In this paper, we prove that the first eigenfunction of the Laplacian for a horo-convex domain $Ω\subset\mathbb H^n$ is super log-concave when $\text{diam}(Ω)$ is not large. Our result is optimal in the sense that there are counterexamples %are constructed for the cases when $Ω$ is not horo-convex or when $\text{diam}(Ω)$ is large respectively |
| title | Super Log-concavity of the First Eigenfunctions for Horo-convex Domains in Hyperbolic Space |
| topic | Analysis of PDEs Differential Geometry 58, 35 |
| url | https://arxiv.org/abs/2510.13072 |