中国科学院数学与系统科学研究院
数学研究所
数学科学全国重点实验室
几何分析研讨班
Speaker: 高东 讲师（北京建筑大学）
Inviter: 杨明轩
Language: 中文
Title: Relative Liouville Rigidity for Lagrangian Self-Similar Submanifolds with Legendrian Boundary
Time & Venue：2026年8月14日（星期五） 14:00-15:00 ZoomID：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≥2), 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.
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