Symplectic Thom conjecture

Let $(X,\omega)$ be a symplectic $4$-manifold, and let $\Sigma\subset (X,\omega)$ be a smoothly embedded symplectic surface. Genus is measured among smoothly embedded surfaces representing the same homology class as $\Sigma$. Symplectic Thom conjecture. The surface $\Sigma$ minimizes genus amongst all smoothly embedded surfaces in its homology class. The statement is presented as a general Thom conjecture arising from adjunction inequalities in symplectic four-manifolds; the supplied text gives no resolution status.