Prescription of finite Dirichlet eigenvalues and area on surface with boundary
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866911783347814400 |
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| author | He, Xiang |
| author_facet | He, Xiang |
| contents | In the present paper, we consider Dirichlet Laplacian on compact surface. We show that for a fixed surface with boundary $X$, a finite increasing sequence of real numbers $0<a_1<a_2<\cdots<a_N$ and a positive number $A$, there exists a metric $g$ on $X$ such that for any integer $1\leq k\leq N$, we have $λ_k^\mathcal{D}(X,g)=a_k$ and $\mathrm{Area}(X,g)=A$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_04190 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Prescription of finite Dirichlet eigenvalues and area on surface with boundary He, Xiang Differential Geometry 58C40, 58J50, 05C50 In the present paper, we consider Dirichlet Laplacian on compact surface. We show that for a fixed surface with boundary $X$, a finite increasing sequence of real numbers $0<a_1<a_2<\cdots<a_N$ and a positive number $A$, there exists a metric $g$ on $X$ such that for any integer $1\leq k\leq N$, we have $λ_k^\mathcal{D}(X,g)=a_k$ and $\mathrm{Area}(X,g)=A$. |
| title | Prescription of finite Dirichlet eigenvalues and area on surface with boundary |
| topic | Differential Geometry 58C40, 58J50, 05C50 |
| url | https://arxiv.org/abs/2308.04190 |