In mathematics, the Wirtinger inequality for 2-forms, named after Wilhelm Wirtinger, states that on a Kähler manifold M, the exterior kth power of the symplectic form (Kähler form) ω, when evaluated on a simple (decomposable) 2k-vector ζ of unit volume, is bounded above by k!. That is, In other words, ωk/k! is a calibration on M. An important corollary is that every complex submanifold of a Kähler manifold is volume minimizing in its homology class.