Abstract
In this paper, 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 the Nitsche (or Hopf) type theorem. Some problems are proposed at the end of this paper.
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Acknowledgements
This work was supported by SPP 2026: Geometry at Infinity of Deutsche Forschungsgemeinschaft. A part of this work was carried out when the second author visited the University of British Columbia. The second author thanks Jingyi Chen and the department for their warm hospitality.
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In Memory of Professor Zhengguo Bai (1916–2015)
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Li, M., Wang, G. & Weng, L. Lagrangian surfaces with Legendrian boundary. Sci. China Math. 64, 1589–1598 (2021). https://doi.org/10.1007/s11425-020-1666-5
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DOI: https://doi.org/10.1007/s11425-020-1666-5