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

Abstract

We classify smoothly immersed Lagrangian $n$-balls, $n\ge 2$, 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].

arXiv comment18 pages. Comments are welcome