Springer eBooks may be purchased by end-customers only and are sold without copy protection (DRM free). Instead, all eBooks include personalized watermarks. This means you can read the Springer eBooks across numerous devices such as Laptops, eReaders, and tablets.
You can pay for Springer eBooks with Visa, Mastercard, American Express or Paypal.
After the purchase you can directly download the eBook file or read it online in our Springer eBook Reader. Furthermore your eBook will be stored in your MySpringer account. So you can always re-download your eBooks.
The only book to systematically explore the equivalence of differential forms
Rigorously presents Hodge decomposition and several versions of the Poincaré lemma
Includes a very rare, extended study of Hölder spaces
Useful resource for graduate students and researchers, requiring only an elementary knowledge of differential geometry and partial and ordinary differential equations
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 φ so that it satisfies the pullback equation: φ*(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 the first 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 Poincaré 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 Hölder 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 Hölder 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.
Content Level »Research
Keywords »Hodge decomposition - Hölder spaces - Poincaré lemma - equivalence of differential forms - global Darboux theorem - local Darboux theorem - pullback equation