Related papers: Dynamique des applications holomorphes propres de …

We investigate problems related with the existence of square integrable holomorphic functions on (unbounded) balanced domains. In particular, we solve the problem of Wiegerinck for balanced domains in dimension two. We also give a…

In this paper, we are concerned with studying the existence of invariant complex manifolds of two-dimensional holomorphic systems. From the geometric singular perturbation theory we know that if a slow-fast system has associated a normally…

This article extends the theorem of the absence of wandering domains from unimodal maps to infinitely period-doubling renormalizable H\'enon-like maps in the strongly dissipative (area contracting) regime. The theorem solves an open problem…

We prove that every bounded strictly $J$-convex region equipped with the Kobayashi metric is hyperbolic in the sense of Gromov. We apply this result to the study of the dynamics of pseudo-holomorphic maps.

We study analysis over infinite dimensional manifolds consisted by sequences of almost K\"ahler manifolds. In particular we develop moduli theory of pseudo holomorphic curves into the spaces with high symmetry. As applications, we study…

We present sufficient conditions so that a conformal map between planar domains whose boundary components are Jordan curves or points has a continuous or homeomorphic extension to the closures of the domains. Our conditions involve the…

Discrete dynamical systems defined by the iteration of a polynomial map of the unit simplex to itself appear in the context of population genetic systems evolving under mutation, recombination and weak selection. Although exceptional…

This paper deals with some geometrical properties of solutions of some semilinear elliptic equations in bounded convex domains or convex rings. Constant boundary conditions are imposed on the single component of the boundary when the domain…

We prove that if $D\subset C^n$ is a bounded domain with real analytic boundary and D is pseudoconvex then the compact open topology in the group of holomorphic automorphisms of D is the topology of uniform convergence on D.

In this paper we study holomorphic properties of infinite dimensional spin factors. Among the infinite dimensional Banach spaces with homogeneous open unit balls, we show that the spin factors are natural outlier spaces in which to ask the…

We give the parameter version of localization theorem for Bergman metric near the boundary points of strictly pseudoconvex domains. The approximation theorem for square integrable holomorphic functions on such domains in the spirit of…

Let M,M' be smooth real hypersurfaces in N-dimensional space and assume that M is k-nondegenerate at a point p in M. We prove that holomorphic mappings that extend smoothly to M, sending a neighborhood of p in M diffeomorphically into M'…

We provide a complete characterization of closed sets with empty interior and positive reach in $\mathbb{R}^2$. As a consequence, we characterize open bounded domains in $\mathbb{R}^2$ whose high ridge and cut locus agree, and hence $C^1$…

In this paper we establish a gap theorem for the complex geometry of smoothly bounded convex domains which informally says that if the complex geometry near the boundary is close to the complex geometry of the unit ball, then the domain…

We study whether the basin of attraction of a sequence of automorphisms of $\mathbb{C}^k$ is biholomorphic to $\mathbb{C}^k$. In particular we show that given any sequence of automorphisms with the same attracting fixed point, the basin is…

In this paper, we characterize weakly pseudoconvex domains of finite type in $\mathbb C^n$ in terms of the boundary behavior of automorphism orbits by using the scaling method.

We study the approximation of J-holomorphic maps continuous to the boundary from ma domain in the complex plane into an almost complex manifold by maps J-holomorphic to the boundary, giving partial results in the non-integrable case. For…

This expository paper is concerned with the properties of proper holomorphic mappings between domains in complex affine spaces. We discuss some of the main geometric methods of this theory, such as the Reflection Principle, the scaling…

The envelope of holomorphy of an arbitrary domain in a two-dimensional Stein manifold is identified with a connected component of the set of equivalence classes of analytic discs immersed into the Stein manifold with boundary in the domain.…

We study the extension of holomorphic functions of bounded type defined on an open subset of a Banach space, to larger domains. For this, we first characterize the envelope of holomorphy of a Riemann domain over a Banach space, with respect…