Related papers: Invariant holomorphic discs in some non-convex dom…

In the paper the complex geodesics of a convex domain in $\mathbb C^n$ are studied. One of the main results of the paper provides certain necessary condition for a holomorphic map to be a complex geodesic for a convex domain in $\mathbb…

We show that the graph of a holomorphic motion of the unit disc cannot be biholomorphic to a strongly pseudoconvex domain in C n .

We construct a finitely dimensional invariant manifold of holomorphic discs attached to a certain class of smooth pseudconvex hypersurfaces of finite type in $\C^2$, generalizing the notion of stationary discs. The discs we construct are…

We study proper holomorphic mappings between strictly pseudoconvex domains with low boundary regularity.

This is a survey on local dynamics of holomorphic maps in one and several complex variables, discussing in particular normal forms and the structure of local stable sets in the non-hyperbolic case, and including several proofs and a vast…

We describe all complex geodesics in convex tube domains. In the case when the base of a convex tube domain does not contain any real line, the obtained description involves the notion of boundary measure of a holomorphic map and it is…

We define and study complex structures and generalizations on spaces consisting of geodesics or harmonic maps that are compatible with the symmetries of these spaces. The main results are about existence and uniqueness of such structures.

This is a survey on the local structure about a fixed point of discrete finite-dimensional holomorphic dynamical systems, discussing in particular the existence of local topological conjugacies to normal forms, and the structure of local…

We give a general procedure to analyze the structure for certain $\mathbb{C}$-Fuchsian subgroups of some non-arithmetic lattices. We will also show that their fundamental domains lie in a complex geodesic, a set homeomorphic to the unit…

We give a survey on higher invariants in noncommutative geometry and their applications to differential geometry and topology.

We show that on convex domains with sufficiently smooth boundary the limit set of non-visible Kobayashi geodesics are contained in a complex face. In two dimensions, this implies the existence of a complex tangential line segment of…

In this paper we describe the algebra of differential invariants for GL(n,C)-structures. This leads to classification of almost complex structures of general positions. The invariants are applied to the existence problem of…

We study the boundary regularity of proper holomorphic mappings between strictly pseudoconvex domains with $C^2$-boundaries.

We survey results arising from the study of domains in C^n with non-compact automorphism group. Beginning with a well-known characterization of the unit ball, we develop ideas toward a consideration of weakly pseudoconvex (and even…

We give, in dimensions three or greater, an example of a bounded, pseudoconvex, circular domain in complex space with smooth real analytic boundary and non-compact automorphism group which is not biholomorphically equivalent to any…

We give a brief survey on local holomorphic dynamics in higher dimensions. The main novelty of this note is that we will organize the material by the "level" of local invariants rather than the type of maps.

We continue the research on the structure of complex geodesics in tube domains over (bounded) convex bases. In some special cases a more explicit form of the geodesics than the existing ones are provided. As one of the consequences of our…

We construct aligned and unaligned stationary perturbation configurations in a composite system of stellar and coplanarly magnetized gaseous singular isothermal discs (SIDs) coupled by gravity. In comparison with SID problems studied…

We study the geodesics on an invariant surface of a three dimensional Riemannian manifold. The main results are: the characterization of geodesic orbits; a Clairaut's relation and its geometric interpretation in some remarkable three…

We show that there are no tight nonholomorphic maps from irreducible domains into exceptional codomains, the only exception being the already known tight nonholomorphic maps from the Poincare disc. This follows up on previous work by the…