A Liouville-type theorem for $2$-Monge-Ampère equation in dimension three
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866912921109397504 |
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| author | Dong, Weisong |
| author_facet | Dong, Weisong |
| contents | We prove that every entire solution with quadratic growth, lying in a suitable cone, to the 2-Monge-Ampère equation on $\mathbb{R}^3$ is a quadratic polynomial. The proof proceeds by first establishing a concavity inequality, and then deriving a Pogorelov-type interior $C^2$ estimate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_20090 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Liouville-type theorem for $2$-Monge-Ampère equation in dimension three Dong, Weisong Analysis of PDEs We prove that every entire solution with quadratic growth, lying in a suitable cone, to the 2-Monge-Ampère equation on $\mathbb{R}^3$ is a quadratic polynomial. The proof proceeds by first establishing a concavity inequality, and then deriving a Pogorelov-type interior $C^2$ estimate. |
| title | A Liouville-type theorem for $2$-Monge-Ampère equation in dimension three |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2602.20090 |