On differentiable area-preserving maps of the plane
F: ℝ2 → ℝ2 is an almost-area-preserving map if: (a) F is a topological embedding, not necessarily surjective; and (b) there exists a constant s > 0 such that for every measurable set B, µ(F(B)) = sµ(B) where µ is the Lebesgue measure. We study when a differentiable map whose Jacobian determinant is nonzero constant to be an almost-area-preserving map. In particular, if for all z, the eigenvalues of the Jacobian matrix DFz are constant, F is an almost-area-preserving map with convex image.
Autor(es):Rabanal, Roland
Año: 2010
Título de la revista: Bulletin of the Brazilian Mathematical Society
Volumen: 41
Número: 1
Página inicial - Página final: 73-82
ISSN: 1678-7544 (print) 1678-7714 (electronic)
Url: https://link.springer.com/article/10.1007%2Fs00574-010-0004-1