@article{Rivière2026, 
author = {Tristan Rivière},
title = {Area Variations Under Legendrian Constraint},
year = {2026},
journal = {Peking Mathematical Journal},
volume = {9},
number = {2},
pages = {293-399},
keywords = {Hamiltonian minimal surfaces, Legendrian surfaces, Minmax, Sasakian manifolds},
url = {https://www.sciopen.com/article/10.1007/s42543-024-00090-y},
doi = {10.1007/s42543-024-00090-y},
abstract = {In any 5-dimensional closed Sasakian manifold, we prove that any minmax operation on the area among Legendrian surfaces is achieved by a continuous conformal Legendrian map from a closed Riemann surface S into N5 equipped with an integer multiplicity bounded in        L    ∞  . Moreover this map, equipped with this multiplicity, satisfies a weak version of the Hamiltonian Minimal Equation. We conjecture that any solution to this equation is a smooth branched Legendrian immersion away from isolated Schoen–Wolfson conical singularities with non-zero Maslov class.}
}