The Pullback Equation for Differential Forms

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 firs