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Rigidity of Lagrangian submanifolds with conformal Maslov form and Legendrian capillary boundary
Abstract
We classify smoothly immersed Lagrangian n-balls, n≥ 2, in the unit ball of ℂn 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].
Related
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BibTeX
@misc{gao2026rigidity,
title = {{Rigidity of Lagrangian submanifolds with conformal Maslov form and Legendrian capillary boundary}},
author = {Dong Gao and Yong Luo and Hui Ma and Jiabin Yin},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.34787},
eprint = {2609.34787},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.34787},
}
RIS
TY - UNPB
TI - Rigidity of Lagrangian submanifolds with conformal Maslov form and Legendrian capillary boundary
AU - Dong Gao
AU - Yong Luo
AU - Hui Ma
AU - Jiabin Yin
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.34787
UR - https://arxiv.org/abs/2609.34787
AB - We classify smoothly immersed Lagrangian n-balls, n≥ 2, in the unit ball of 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].
ER -