Incompressibility and global inversion
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Global injectivity, global invertibility, Hadamard's theoremAbstrakt
Given a local diffeomorphism $f\colon \mathbb{R}^n\to \mathbb{R}^n$, we consider certain incompressibility conditions on the parallelepiped $Df(x)([0,1]^n)$ which imply that the pre-image of an affine subspace is non-empty and has trivial homotopy groups. These conditions are then used to establish criteria for $f$ to be globally invertible, generalizing in all dimensions the previous results of M. Sabatini.Pobrania
Opublikowane
2010-04-23
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BALREIRA, Eduardo Cabral. Incompressibility and global inversion. Topological Methods in Nonlinear Analysis [online]. 23 kwiecień 2010, T. 35, nr 1, s. 69–76. [udostępniono 22.7.2024].
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