Einstein Metrics and Complex Structures.
In 2001, B. Malgrange defines the D-envelope or galoisian envelope of an analytical dynamical system. Roughly speaking, this is the algebraic hull of the dynamical system. In this short article, the D-envelope of a rational map R: P1 --> P1 is computed. The rational maps characterised by a finitness property of their D-envelope appear to be the integrable ones.
It is shown that if a manifold admits an exact symplectic form, then its Poisson Lie algebra has non trivial formal deformations and the manifold admits star-products. The non-formal derivations of the star-products and the deformations of the Poisson Lie algebra of an arbitrary symplectic manifold are studied.
We prove that on an asymptotically Euclidean boundary groupoid, the heat kernel of the Laplacian is a smooth groupoid pseudo-differential operator.