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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2309.09432 |
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| _version_ | 1866908396879347712 |
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| author | Tsai, Chung-Jun Tsui, Mao-Pei Wang, Mu-Tao |
| author_facet | Tsai, Chung-Jun Tsui, Mao-Pei Wang, Mu-Tao |
| contents | Given an entire $C^2$ function $u$ on $\mathbb{R}^n$, we consider the graph of $D u$ as a Lagrangian submanifold of $\mathbb{R}^{2n}$, and deform it by the mean curvature flow in $\mathbb{R}^{2n}$. This leads to the special Lagrangian evolution equation, a fully nonlinear Hessian type PDE. We prove long-time existence and convergence results under a 2-positivity assumption of $(I+(D^2 u)^2)^{-1}D^2 u$. Such results were previously known only under the stronger assumption of positivity of $D^2 u$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_09432 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Entire solutions of two-convex Lagrangian mean curvature flows Tsai, Chung-Jun Tsui, Mao-Pei Wang, Mu-Tao Differential Geometry 53C44 Given an entire $C^2$ function $u$ on $\mathbb{R}^n$, we consider the graph of $D u$ as a Lagrangian submanifold of $\mathbb{R}^{2n}$, and deform it by the mean curvature flow in $\mathbb{R}^{2n}$. This leads to the special Lagrangian evolution equation, a fully nonlinear Hessian type PDE. We prove long-time existence and convergence results under a 2-positivity assumption of $(I+(D^2 u)^2)^{-1}D^2 u$. Such results were previously known only under the stronger assumption of positivity of $D^2 u$. |
| title | Entire solutions of two-convex Lagrangian mean curvature flows |
| topic | Differential Geometry 53C44 |
| url | https://arxiv.org/abs/2309.09432 |