Work

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

Year: 2026

Type: preprint

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].

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.34787

Authors: Gao, Dong, Luo, Yong, Ma, Hui, Yin, Jiabin

Institutions: Beijing University of Civil Engineering and Architecture, Chongqing University of Technology, Xinyang Normal University, Tsinghua University

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Natural Science Foundation of Henan Province

Awards: G214142170, G2687531736, G3804335326

OpenAlex ID: W7214801202

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