We deal with kernel convergence of domains in Cn which are biholomorphically equivalent to the unit ball B. We also prove that there is an equivalence between the convergence on compact sets of biholomorphic mappings on B, which satisfy a growth theorem, and the kernel convergence. Moreover, we obtain certain consequences of this equivalence in the study of Loewner chains and of starlike and co...

"In this paper, two subclasses of biholomorphic starlike mappings named Janowski and almost with complex parameters are introduced studied. We determine $M$ such that holomorphic $f$ which satisfy the condition $\|Df(z)-I\|\le M$, $z\in B^n$, starlike, respectively starlike. also derive sufficient conditions for normalized (expressed in terms their coefficient bounds) to belong one mentioned ab...

By making use of our previous result on a localization principle for biholomorphic mappings between equidimensional Fock-Bargmann-Hartogs domains in ℂn×ℂm with m≥2 and the same technique as study ℂn×ℂ, this paper we establish characterization biholomorphicity holomorphic self-mappings generalized domains. As special case this, obtain main recent by Guo, Feng Bi.

In this article, we exhibit a large class of Banach spaces whose open unit balls are bounded symmetric homogeneous domains. These Banach spaces, which we call J*-algebras, are linear spaces of operators mapping one Hilbert space into another and have a kind of Jordan tripte product structure. In particular, all Hilbert spaces and all B*--algebras are J*-algebras. Moreover, all four types of the...

This paper concerns the geometry of noncommutative domains and analytic free maps. These maps are free analogs of classical analytic functions in several complex variables, and are defined in terms of noncommuting variables amongst which there are no relations they are free variables. Analytic free maps include vector-valued polynomials in free (noncommuting) variables and form a canonical clas...

Problem: Determine the complex structure of the stable manifolds of f . It is not hard to see, using f(W s p ) = W s fp, that W s p is a monotone union of balls, and this in turn implies [Br] that it is diffeomorphic to real Euclidean space. Moreover, by the contracting nature of the dynamics, one sees that the Kobayashi pseudometric of W s p vanishes identically. However, when dim(W s p ) ≥ 3,...

These manifolds M are complex tori up to nite etale coverings, or satisfy both inequalities (M) < n 3 and q(M) < n 3.