By Gyula Csató,Bernard Dacorogna,Olivier Kneuss
An very important query in geometry and research is to grasp whilst k-forms f and g are similar via a transformation of variables. the matter is as a result to discover a map φ so that it satisfies the pullback equation: φ*(g) = f.
In extra actual phrases, the query into account may be noticeable as an issue of mass transportation. the matter has obtained substantial realization within the situations k = 2 and k = n, yet less while three ≤ k ≤ n–1. the current monograph offers the first finished research of the equation.
The paintings starts by way of recounting a variety of homes of external kinds and differential kinds that turn out necessary in the course of the publication. From there it is going directly to current the classical Hodge–Morrey decomposition and to provide a number of models of the Poincaré lemma. The center of the ebook discusses the case k = n, after which the case 1≤ k ≤ n–1 with specific recognition at the case k = 2, that's basic in symplectic geometry. particular emphasis is given to optimum regularity, worldwide effects and boundary information. The final a part of the paintings discusses Hölder areas intimately; the entire effects awarded listed below are basically classical, yet can't be present in a unmarried ebook. This part could function a reference on Hölder areas and hence can be worthwhile to mathematicians well past people who find themselves basically attracted to the pullback equation.
The Pullback Equation for Differential types is a self-contained and concise monograph meant for either geometers and analysts. The publication could function a worthwhile reference for researchers or a supplemental textual content for graduate classes or seminars.
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Extra info for The Pullback Equation for Differential Forms: 83 (Progress in Nonlinear Differential Equations and Their Applications)
The Pullback Equation for Differential Forms: 83 (Progress in Nonlinear Differential Equations and Their Applications) by Gyula Csató,Bernard Dacorogna,Olivier Kneuss