Wirtinger inequality (2-forms)

For other inequalities named after Wirtinger, see Wirtinger's inequality.

In mathematics, the Wirtinger inequality for 2-forms, named after Wilhelm Wirtinger, states that the exterior $scriptstylenu$^th power of the standard symplectic form ω, when evaluated on a simple (decomposable) $(2nu)$-vector ζ of unit volume, is bounded above by $scriptstylenu!$. In other words,

$omega^nu(zeta)\; leq\; nu\; !,.$

See also

• 2-form
• Gromov's inequality for complex projective space
• Systolic geometry