Weiyong He

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20232025

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math.DG2024

Convergence of the hypersymplectic flow on $T^{4}$ with $T^{3}$ -symmetry

Joel Fine, Weiyong He, Chengjian Yao

A hypersymplectic structure on a 4-manifold is a triple $ω_{1}, ω_{2}, ω_{3}$ of 2-forms for which every non-trivial linear combination $a^{1} ω_{1} + a^{2} ω_{2} + a^{3} ω_{3}$ is a symplectic form.…

math.DG2023

Nonlinear Hodge flows in symplectic geometry

Weiyong He

Given a symplectic class $[ω]$ on a four torus $T^{4}$ (or a $K 3$ surface), a folklore problem in symplectic geometry is whether symplectic forms in $[ω]$ are isotropic to each other…

Convergence of the hypersymplectic flow on T4 with T3-symmetry

Nonlinear Hodge flows in symplectic geometry

Convergence of the hypersymplectic flow on $T^{4}$ with $T^{3}$ -symmetry