We prove some normality criteria for families of meromorphic mappings of a domain into ℂPⁿ under a condition on the inverse images of moving hypersurfaces.
First, we give some characterizations of J-hyperbolic points for almost complex manifolds. We apply these characterizations to show that the hyperbolic embeddedness of an almost complex submanifold follows from relative compactness of certain spaces of continuous extensions of pseudoholomorphic curves defined on the punctured unit disc. Next, we define uniformly normal families of pseudoholomorphic curves. We prove extension-convergence theorems for these families similar to those obtained by Kobayashi,...
We show that a complex normal surface singularity admitting a contracting automorphism is necessarily quasihomogeneous. We also describe the geometry of a compact complex surface arising as the orbit space of such a contracting automorphism.
We establish a Poincaré-Dulac theorem for sequences of holomorphic contractions whose differentials split regularly. The resonant relations determining the normal forms hold on the moduli of the exponential rates of contraction. Our results are actually stated in the framework of bundle maps.Such sequences of holomorphic contractions appear naturally as iterated inverse branches of endomorphisms of . In this context, our normalization result allows to estimate precisely the distortions of ellipsoids...
Let f be a germ of plane curve, we define the δ-degree of sufficiency of f to be the smallest integer r such that for anuy germ g such that j(r) f = j(r) g then there is a set of disjoint annuli in S3 whose boundaries consist of a component of the link of f and a component of the link of g. We establish a formula for the δ-degree of sufficiency in terms of link invariants of plane curves singularities and, as a consequence of this formula, we obtain that the δ-degree of sufficiency is equal to the...
Dans cet article, en utilisant les algèbres de Jordan euclidiennes, nous étudions l’espace de Hardy d’un espace symétrique de type Cayley . Nous montrons que le noyau de Cauchy-Szegö de s’exprime comme somme d’une série faisant intervenir la fonction de Harish-Chandra de l’espace symétrique riemannien , la fonction de l’espace symétrique -dual de et les fonctions sphériques de l’espace symétrique ordonné . Nous établissons, dans le cas où la dimension de l’algèbre de Jordan associée...