Speaker: 高东讲师，北京建筑大学

Inviter: 杨明轩

Title: Relative Liouville Rigidity for Lagrangian Self-Similar Submanifolds with Legendrian Boundary

Language: Chinese

Time & Venue: 2026.08.14 14:00-15:00 腾讯会议：424-194-573

Abstract: We study compact Lagrangian self-similar immersions in the unit ball with Legendrian boundary. We prove that vanishing of the relative Liouville class forces the immersion to be an equatorial Lagrangian disk, yielding rigidity in particular for exact immersions with connected boundary. Using a boundary flux identity and boundary unique continuation, we further obtain rigidity under several natural boundary conditions, including the free-boundary case. In dimension two, our results recover the smooth disk theorem of Li–Wang–Weng and the free-boundary theorem of Luo–Sun, while extending these rigidity phenomena to higher dimensions and the self-similar setting. We also construct, in every dimension (n\ge2), compact embedded exact Lagrangian examples with two Legendrian capillary boundary components and nonzero relative Liouville class. This is joint work with Hui Ma and Zeke Yao.