Entanglement principle for fractional Laplacian on hyperbolic spaces and applications to inverse problem
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908881782833152 |
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| author | Lin, Yi-Hsuan |
| author_facet | Lin, Yi-Hsuan |
| contents | We establish an entanglement principle for fractional powers of the Laplace-Beltrami operator on hyperbolic space $\mathbb H^n$, $n\ge 2$. More precisely, we prove that if finitely many distinct noninteger powers of $-Δ_{\mathbb H^n}$, acting on functions that vanish on a common nonempty open set, satisfy a linear dependence relation on that set, then each of these functions must vanish identically on $\mathbb H^n$. This extends the recently developed entanglement principle for the fractional Laplacian on $\mathbb R^n$ to the negatively curved setting of hyperbolic space. As an application, we derive global uniqueness results for inverse problems associated with fractional polyharmonic equations on $\mathbb H^n$, including a fractional Calderón problem. The proof relies on the heat semigroup representation of fractional powers together with sharp global heat kernel estimates on hyperbolic space. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_11702 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Entanglement principle for fractional Laplacian on hyperbolic spaces and applications to inverse problem Lin, Yi-Hsuan Analysis of PDEs We establish an entanglement principle for fractional powers of the Laplace-Beltrami operator on hyperbolic space $\mathbb H^n$, $n\ge 2$. More precisely, we prove that if finitely many distinct noninteger powers of $-Δ_{\mathbb H^n}$, acting on functions that vanish on a common nonempty open set, satisfy a linear dependence relation on that set, then each of these functions must vanish identically on $\mathbb H^n$. This extends the recently developed entanglement principle for the fractional Laplacian on $\mathbb R^n$ to the negatively curved setting of hyperbolic space. As an application, we derive global uniqueness results for inverse problems associated with fractional polyharmonic equations on $\mathbb H^n$, including a fractional Calderón problem. The proof relies on the heat semigroup representation of fractional powers together with sharp global heat kernel estimates on hyperbolic space. |
| title | Entanglement principle for fractional Laplacian on hyperbolic spaces and applications to inverse problem |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2603.11702 |