On Liouville's theorem for the Hessian quotient equation $σ_2/σ_1$
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866914333079896064 |
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| author | Lu, Siyuan Sroka, Marcin |
| author_facet | Lu, Siyuan Sroka, Marcin |
| contents | We prove Liouville's theorem for semi-convex entire solutions to Hessian quotient equation $σ_2/σ_1=1$ in $\mathbb{R}^n$. The proof is based on the observation that after rewriting the quotient operator as the $σ_2$ operator, acting on a new function, one can refer to the recent result of Shankar and Yuan on Liouville's theorem for $σ_2$ equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_14946 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Liouville's theorem for the Hessian quotient equation $σ_2/σ_1$ Lu, Siyuan Sroka, Marcin Analysis of PDEs 35B53, 35J60, 35J15 We prove Liouville's theorem for semi-convex entire solutions to Hessian quotient equation $σ_2/σ_1=1$ in $\mathbb{R}^n$. The proof is based on the observation that after rewriting the quotient operator as the $σ_2$ operator, acting on a new function, one can refer to the recent result of Shankar and Yuan on Liouville's theorem for $σ_2$ equation. |
| title | On Liouville's theorem for the Hessian quotient equation $σ_2/σ_1$ |
| topic | Analysis of PDEs 35B53, 35J60, 35J15 |
| url | https://arxiv.org/abs/2602.14946 |