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Original Article | Open Access

Area Variations Under Legendrian Constraint

ETH Zürich D-MATH: Eidgenossische Technische Hochschule Zurich Departement Mathematik, Zürich, Switzerland
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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.

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Peking Mathematical Journal
Pages 293-399

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Cite this article:
Rivière, T. Area Variations Under Legendrian Constraint. Peking Math J 9, 293-399 (2026). https://doi.org/10.1007/s42543-024-00090-y

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Received: 02 January 2024
Revised: 06 June 2024
Accepted: 15 August 2024
Published: 17 February 2025
© The Author(s) 2025

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