Dynamical Stability of Minimal Lagrangians in Kähler-Einstein Manifolds of Non-Positive Curvature
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866917687430479872 |
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| author | Lee, Ping-Hung Tsai, Chung-Jun |
| author_facet | Lee, Ping-Hung Tsai, Chung-Jun |
| contents | It is known that minimal Lagrangians in Kähler--Einstein manifolds of non-positive scalar curvature are linearly stable under Hamiltonian deformations. We prove that they are also stable under the Lagrangian mean curvature flow, and therefore establish the equivalence between linear stability and dynamical stability.
Specifically, if one starts the mean curvature flow with a Lagrangian which is $C^1$-close and Hamiltonian isotopic to a minimal Lagrangian, the flow exists smoothly for all time, and converges to that minimal Lagrangian. Due to the work of Neves [Ann. of Math. 2013], this cannot be true for $C^0$-closeness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_04602 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dynamical Stability of Minimal Lagrangians in Kähler-Einstein Manifolds of Non-Positive Curvature Lee, Ping-Hung Tsai, Chung-Jun Differential Geometry Symplectic Geometry It is known that minimal Lagrangians in Kähler--Einstein manifolds of non-positive scalar curvature are linearly stable under Hamiltonian deformations. We prove that they are also stable under the Lagrangian mean curvature flow, and therefore establish the equivalence between linear stability and dynamical stability. Specifically, if one starts the mean curvature flow with a Lagrangian which is $C^1$-close and Hamiltonian isotopic to a minimal Lagrangian, the flow exists smoothly for all time, and converges to that minimal Lagrangian. Due to the work of Neves [Ann. of Math. 2013], this cannot be true for $C^0$-closeness. |
| title | Dynamical Stability of Minimal Lagrangians in Kähler-Einstein Manifolds of Non-Positive Curvature |
| topic | Differential Geometry Symplectic Geometry |
| url | https://arxiv.org/abs/2406.04602 |