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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.00748 |
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Table of Contents:
- Let $Ω\subset \mathbb{C}^2$ be a smooth domain. We establish conditions under which a weakly conformal, branched $Ω$-free boundary Hamiltonian stationary Lagrangian immersion $u$ of a disc in $\mathbb{C}^2$ is a $Ω$-free boundary minimal immersion. We deduce that if $u$ is a weakly conformal, branched $B_1(0)$-free boundary Hamiltonian stationary Lagrangian immersion of a disc with Legendrian boundary data, then $u(D^2)$ must be a Lagrangian equatorial plane disc. We also present examples of $Ω$-free boundary Hamiltonain stationary discs, demonstrating the optimality of our assumptions.