Applications in Geometric Measure Theory
Numerous minimality results for complex analytic manifolds are based on the Wirtinger inequality for 2-forms. A succinct proof may be found in Herbert Federer's classic text Geometric Measure Theory. The Wirtinger inequality is also a key ingredient in Gromov's inequality for complex projective space in systolic geometry.
Read more about this topic: Differential Form
Famous quotes containing the words geometric, measure and/or theory:
“New York ... is a city of geometric heights, a petrified desert of grids and lattices, an inferno of greenish abstraction under a flat sky, a real Metropolis from which man is absent by his very accumulation.”
—Roland Barthes (19151980)
“I am not the measure of creation.
This is beyond me, this fish.
His God stands outside my God.”
—D.H. (David Herbert)
“The theory of rights enables us to rise and overthrow obstacles, but not to found a strong and lasting accord between all the elements which compose the nation.”
—Giuseppe Mazzini (18051872)