c2中的自由边界哈密顿静止拉格朗日盘。

IF 1.2 2区数学 Q1 MATHEMATICS

Journal of Geometric Analysis Pub Date : 2025-01-01 Epub Date: 2025-04-04 DOI:10.1007/s12220-025-01962-0

Filippo Gaia

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引用次数: 0

摘要

设Ω∧c2为光滑域。我们建立了在c2中一个弱共形，分支的Ω自由边界哈密顿平稳拉格朗日浸入u是Ω自由边界最小浸入的条件。我们推导出，如果u是一个具有勒让边界的盘的弱共形，分支b2(0)自由边界哈密顿平稳拉格朗日浸没，则u （d2）是一个拉格朗日赤道平面盘。此外，我们给出了Ω自由边界哈密顿平稳盘的例子，证明了我们假设的最优性。

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Free Boundary Hamiltonian Stationary Lagrangian Discs in C 2.

Let $Ω \subset C^{2}$ 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 $C^{2}$ 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, then $u (D^{2})$ is a Lagrangian equatorial plane disc. Furthermore, we present examples of $Ω$ -free boundary Hamiltonian stationary discs, demonstrating the optimality of our assumptions.

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来源期刊

Journal of Geometric Analysis 数学-数学

CiteScore

2.00

自引率

9.10%

发文量

290

审稿时长

3 months

期刊介绍： JGA publishes both research and high-level expository papers in geometric analysis and its applications. There are no restrictions on page length.