Wirtinger inequality (2-forms)

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 scriptstyle uth power of the standard symplectic form ω, when evaluated on a simple (decomposable) (2 u)-vector ζ of unit volume, is bounded above by scriptstyle u!. In other words,

: omega^ u(zeta) leq u !,.

ee also

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


Wikimedia Foundation. 2010.

Игры ⚽ Нужно сделать НИР?

Look at other dictionaries:

  • Wirtinger's inequality — is either of two inequalities named after Wilhelm Wirtinger:* Wirtinger s inequality for functions * Wirtinger inequality (2 forms) …   Wikipedia

  • Wilhelm Wirtinger — (15 July 1865 ndash; 15 January 1945) was an Austrian mathematician. He was born at Ybbs on the Danube and studied at the University of Vienna, where he received his doctorate in 1887, and his habilitation in 1890. Wirtinger was greatly… …   Wikipedia

  • Gromov's inequality for complex projective space — In Riemannian geometry, Gromov s optimal stable 2 systolic inequality is the inequality: mathrm{stsys} 2{}^n leq n!;mathrm{vol} {2n}(mathbb{CP}^n),valid for an arbitrary Riemannian metric on the complex projective space, where the optimal bound… …   Wikipedia

  • List of inequalities — This page lists Wikipedia articles about named mathematical inequalities. Inequalities in pure mathematics =Analysis= * Askey–Gasper inequality * Bernoulli s inequality * Bernstein s inequality (mathematical analysis) * Bessel s inequality *… …   Wikipedia

  • List of mathematics articles (W) — NOTOC Wad Wadge hierarchy Wagstaff prime Wald test Wald Wolfowitz runs test Wald s equation Waldhausen category Wall Sun Sun prime Wallenius noncentral hypergeometric distribution Wallis product Wallman compactification Wallpaper group Walrasian… …   Wikipedia

  • List of differential geometry topics — This is a list of differential geometry topics. See also glossary of differential and metric geometry and list of Lie group topics. Contents 1 Differential geometry of curves and surfaces 1.1 Differential geometry of curves 1.2 Differential… …   Wikipedia

  • Symplectic manifold — In mathematics, a symplectic manifold is a smooth manifold, M, equipped with a closed nondegenerate differential 2 form, ω, called the symplectic form. The study of symplectic manifolds is called symplectic geometry or symplectic topology.… …   Wikipedia

  • Differential form — In the mathematical fields of differential geometry and tensor calculus, differential forms are an approach to multivariable calculus that is independent of coordinates. Differential forms provide a better[further explanation needed] definition… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”