M ar 2 00 9 A note on the divergence - free Jacobian Conjecture in IR 2 ∗ M . Sabatini
نویسنده
چکیده
We give a shorter proof to a recent result by Neuberger [11], in the real case. Our result is essentially an application of the global asymptotic stability Jacobian Conjecture. We also extend some of the results presented in [11].
منابع مشابه
Real Divergence-free Jacobian Maps Are Shear Maps *
We show that divergence-free jacobian maps, recently considered in [11], [14], are actually shear maps.
متن کاملThe Divergence-free Jacobian Conjecture in Dimension Two
A special case, called the divergence-free case, of the Jacobian Conjecture in dimension two is proved. This note outlines an argument for a special case of the Jacobian conjecture in dimension two: Suppose F : C → C is a polynomial so that F (0) = 0, F ′(0) = I, det(F ′(z)) = 1, z ∈ C. (1) where I is the identity transformation on C. Write F (x, y) = ( r(x, y) + x s(x, y) + y ) , (x, y) ∈ C wh...
متن کاملar X iv : m at h - ph / 0 31 00 64 v 1 2 9 O ct 2 00 3 On the monotonicity conjecture for the curvature of the Kubo - Mori metric ∗
The canonical correlation or Kubo-Mori scalar product on the state space of a finite quantum system is a natural generalization of the classical Fisher metric. This metric is induced by the von Neumann entropy or the relative entropy of the quantum mechanical states. An important conjecture of Petz that the scalar curvature of the state space with Kubo-Mori scalar product as Riemannian metric i...
متن کاملM ar 2 00 9 On the Jacobian of the harmonic moment map
In this paper we represent harmonic moments in the language of transfinite functions, that is projective limits of polynomials in infinitely many variables. We obtain also an explicit formula for the Jacobian of a generalized harmonic moment map. Mathematics Subject Classification (2000). 13B35; 30E05; 47A57.
متن کامل. A P ] 1 5 M ar 2 00 6 Conservation laws for conformal invariant variational problems
We succeed in writing 2-dimensional conformally invariant nonlinear elliptic PDE (harmonic map equation, prescribed mean curvature equations...etc) in divergence form. This divergence free quantities generalize to target manifolds without symmetries the well known conservation laws for harmonic maps into homogeneous spaces. From this form we can recover, without the use of moving frame, all the...
متن کامل