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arXiv · 2609.34787

Rigidity of Lagrangian submanifolds with conformal Maslov form and Legendrian capillary boundary

Dong Gao·Yong Luo·Hui Ma·Jiabin Yin
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Abstract

We classify smoothly immersed Lagrangian $n$-balls, $n\geq 2$, in the unit ball of $\mathbb{C}^n$ with conformal Maslov form and Legendrian capillary boundary. The image of every such immersion is either an equatorial Lagrangian disk or is contained in a Whitney sphere centered at the origin. In dimension two, this confirms a conjecture of Li, Wang and Weng [Sci. China Math. 2021].

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Dong Gao, Yong Luo, Hui Ma, Jiabin Yin. 2026-09-28. Rigidity of Lagrangian submanifolds with conformal Maslov form and Legendrian capillary boundary. https://arxiv.org/abs/2609.34787

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