Joel Fine

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math.DG2025

Seiberg-Witten equations in all dimensions

Joel Fine, Partha Ghosh

Starting with an $n$ -dimensional oriented Riemannian manifold with a Spin-c structure, we describe an elliptic system of equations which recover the Seiberg-Witten equations when $…

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 $I ¨ _{1}, I ¨ _{2}, I ¨ _{3}$ of 2-forms for which every non-trivial linear combination $a^{1} I ¨ _{1} + a^{2} I ¨ _{2} + a^{3} I ¨ _{3}$ is a symplectic…

Seiberg-Witten equations in all dimensions

Convergence of the hypersymplectic flow on T4 with T3-symmetry

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