One complex variable from the several variables point of view

We discuss basic properties of holomorphic functions of one complex variable from the point of view of the theory of several complex variables.     

Hilbert schemes of surfaces are dense in moduli

We prove that the locus of Hilbert schemes of n points on a projective K 3 surface is dense in the moduli space of irreducible holomorphic symplectic manifolds of that deformation type. The analogous result for generalized Kummer manifolds is proven as well. Along the way we prove an integral constraint on the monodromy group of generalized Kummer manifolds.     

Generalized holomorphic processes and differentiability

Holomorphic processes are studied when the parameter set is a general finite atomless separable measure space, using the differentiation operator and Malliavin calculus. Generalized martingales are connected with differentiable processes. In the two-parameter case, these methods give a new simpler proof of the characterization of holomorphic processes by power series expansion.This work has been done while D. Nualart was staying as a visitor at Bar-Ilan University.     

Approximating fixed points of holomorphic mappings in the Hilbert ball

We approximate fixed points of holomorphic and ρ-nonexpansive self-mappings of the Hilbert ball using both continuous and discrete schemes.     

一类Khler流形上的全纯映射

本文利用Ｋａｈｌｅｒ流形上的Ｌａｐｌａｃｅ算子,给出了一类全纯映射的增长性结论     

高维复域中非线性全特征方程的全纯解

本文在全纯函数类中研究了一类定义在高维复域中的非线性奇异偏微分方程,在一定条件下,证明了其局部全纯解的存在性与唯一性．     

Geometric bounds on the linearization domain and analytic dependence on parameters for families of analytic vector fields in a neighborhood of a singular point

We study families of holomorphic vector fields, holomorphically depending on parameters, in a neighborhood of an isolated singular point. When the singular point is in the Poincaré domain for every vector field of the family we prove, through a modification of classical Sternberg's linearization argument, cf. Nelson (1969) [7] too, analytic dependence on parameters of the linearizing maps and geometric bounds on the linearization domain: each vector field of the family is linearizable inside the smallest Euclidean sphere which is not transverse to the vector field, cf. Brushlinskaya (1971) [2], Ilyashenko and Yakovenko (2008) [5] for related results. We also prove, developing ideas in Martinet (1980) [6], a version of Brjuno's Theorem in the case of linearization of families of vector fields near a singular point of Siegel type, and apply it to study some 1-parameter families of vector fields in two dimensions.     

一类广义Hartogs三角形之间逆紧映射的分类

本文主要证明一类广义Hartogs三角形之间的逆紧全纯映射在相差全纯自同构的意义下是唯一的。     

Real analyticity of Hausdorff dimension for higher dimensional hyperbolic graph directed Markov systems

In this paper we prove that the Hausdorff dimension function of the limit sets of strongly regular, hyperbolic, conformal graph directed Markov systems living in higher dimensional Euclidean spaces , , and with an underlying finitely irreducible incidence matrix is real-analytic. Research of M. Roy was supported by NSERC (Natural Sciences and Engineering Research Council of Canada). Research of M. Urbański was supported in part by the NSF Grant DMS 0400481.