Lagrangian surfaces with Legendrian boundary
Differential Geometry
2025-05-28 v3
Abstract
In this note, we first introduce a boundary problem for Lagrangian submanifolds, analogous to the problem for free boundary hypersurfaces and capillary hypersurfaces. Then we present several interesting examples of Lagrangian submanifolds satisfying this boundary condition and we prove a Lagrangian version of Nitsche (or Hopf) type theorem. Some problems are proposed at the end of this note.
Cite
@article{arxiv.1910.05397,
title = {Lagrangian surfaces with Legendrian boundary},
author = {Mingyan Li and Guofang Wang and Liangjun Weng},
journal= {arXiv preprint arXiv:1910.05397},
year = {2025}
}
Comments
The final version, accepted for publication in SCIENCE CHINA Mathematics