1. A Geometric flow towards hamiltonian stationary submanifolds
- Author
-
Chen, Jingyi and Warren, Micah
- Subjects
Mathematics - Differential Geometry ,Mathematics - Analysis of PDEs ,53E40, 58J35, 35K25 - Abstract
In this paper, we introduce a geometric flow for Lagrangian submanifolds in a K\"ahler manifold that stays in its initial Hamiltonian isotopy class and is a gradient flow for volume. The stationary solutions are the Hamiltonian stationary Lagrangian submanifolds. The flow is not strictly parabolic but it corresponds to a fourth order strictly parabolic scalar equation in the cotangent bundle of the submanifold via Weinstein's Lagrangian neighborhood theorem. For any compact initial Lagrangian immersion, we establish short-time existence, uniqueness, and higher order estimates when the second fundamental forms are uniformly bounded up to time $T$., Comment: 32 pages
- Published
- 2024