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arXiv · 2306.10633

Area Variations under Legendrian Constraint

Tristan Rivière
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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 $N^5$ equipped with an integer multiplicity bounded in $L^\infty$. 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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Tristan Rivière. 2023-06-18. Area Variations under Legendrian Constraint. https://arxiv.org/abs/2306.10633

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