What question did this study set out to answer?

This research aims to identify criteria under which bounded almost complex curves minimize genus among surfaces in 4-manifolds.

Relative Thom conjectures, symplectic and beyond

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We establish a criterion for minimizing genus of curves in 4-manifolds, thus supporting the symplectic Thom conjecture and revealing knot invariants.

This research aims to identify criteria under which bounded almost complex curves minimize genus among surfaces in 4-manifolds.
Established a criterion for genus minimization in almost complex 4-manifolds with specific homology classes and boundary conditions.
Analyzed obstructions from knot Floer homology related to bounding symplectic surfaces.
Examined cases involving plane fields and non-symplectic fillings, particularly in contact 3-manifolds.
Demonstrated that certain symplectic surfaces minimize slice genus for their boundary with a positive Ozsváth-Szabó invariant.
Confirmed the relative symplectic Thom conjecture as an immediate consequence of the findings.
Proposed that the tightness of contact structures relates to symplecto-geometric properties.

Hedden et al. (2026) studied this question.

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We establish a criterion for minimizing genus of curves in 4-manifolds, thus supporting the symplectic Thom conjecture and revealing knot invariants.