An important question in geometry and analysis is to know when
two "k"-forms "f "and g are equivalent through a change of
variables. The problem is therefore to find a map " "so that it
satisfies the pullback equation: " ""*"("g") = "f."
In more physical terms, the question under consideration can be
seen as a problem of mass transportation. The problem has received
considerable attention in the cases "k "= 2 and "k "= "n," but much
less when 3 "k " "n"-1. The present monograph provides thefirst
comprehensive study of the equation.
The work begins by recounting various properties of exterior
forms and differential forms that prove useful throughout the book.
From there it goes on to present the classical Hodge-Morrey
decomposition and to give several versions of the Poincare lemma.
The core of the book discusses the case "k "= "n," and then the
case 1 "k " "n"-1 with special attention on the case "k "= 2, which
is fundamental in symplectic geometry. Special emphasis is given to
optimal regularity, global results and boundary data. The last part
of the work discusses Holder spaces in detail; all the results
presented here are essentially classical, but cannot be found in a
single book. This section may serve as a reference on Holder spaces
and therefore will be useful to mathematicians well beyond those
who are only interested in the pullback equation.
"The Pullback Equation for Differential Forms "is a
self-contained and concise monograph intended for both geometers
and analysts. The book may serve as a valuable reference for
researchers or a supplemental text for graduate courses or
seminars."
General
Is the information for this product incomplete, wrong or inappropriate?
Let us know about it.
Does this product have an incorrect or missing image?
Send us a new image.
Is this product missing categories?
Add more categories.
Review This Product
No reviews yet - be the first to create one!