In this article, published in Duke Math. J. the authors developed a new method for contructing holomorphic maps by the tehnique of gluing holomorphic sprays on Cartan pairs of strongly pseudoconvex Stein domains. This technique had been to some extent developed in earlier works of M. Gromov and the second author, they obtained a substantial improvement that allows control of regularity up to the boundaries of respective domains.
COBISS.SI-ID: 14351705
In the first of these articles the author proved that the classical Oka property of a complex manifold Y is equivalent to a Runge type approximation property concerning entire holomorphic mappings from complex Euclidean spaces to Y, with approximation on compact convex subsets (the "convex approximation property, CAP). This answered an outstanding problem of M.Gromov from 1989. The article is published in the elite journal Annals of Math. This was continued by F. Forstnerič and M. Slapar ( Math. Zeitschrift 256, 2007, who proved the soft Oka priciple without any conditions on Y.
COBISS.SI-ID: 13908825
The authors consider Riemann-Hilbert boundary value problems for functions on bordered Riemann surfaces, for a smooth family ?_z , of smooth Jordan curves in the complex plane which all contain 0 in their interior, where z runs along the boundary of a bordered Riemann surface. In the first article the authors generalize the notion of Ahlfors function to given boundary data and in the second article the authors solve a nonlinear boundary value problem for solutions of a quasilinear Cauchy-Riemann equation on R.
COBISS.SI-ID: 1422780
In the work under consideration it is proved that the L^p norms of powers T^n of the classical Ahlfors-Beurling operator grow as n^{1-2/p}(p-1). The estimate is double-sided and thus sharp simultaneously in n and p. The work appeared in a very renowned journal, J. Math. Pures Appl.
COBISS.SI-ID: 14157657
The author constructs a new Hamiltonian structure of the Maxwell-Bloch equations. This system describes a continuous chain of interacting C. Neumann oscillators on the 3-sphere and the interaction is of magnetic type. Configuration space of the system is the loop group over SU(2). The author constructs a new, simpler Hamiltonian structure of the Maxwell-Bloch equations.
COBISS.SI-ID: 1380273
In this article, published in Duke Math. J. the authors developed a new method for contructing holomorphic maps by the tehnique of gluing holomorphic sprays on Cartan pairs of strongly pseudoconvex Stein domains. This technique had been to some extent developed in earlier works of M. Gromov and the second author, they obtained a substantial improvement that allows control of regularity up to the boundaries of respective domains.
COBISS.SI-ID: 14351705
The authors consider Riemann-Hilbert boundary value problems for functions on bordered Riemann surfaces, for a smooth family ?_z , of smooth Jordan curves in the complex plane which all contain 0 in their interior, where z runs along the boundary of a bordered Riemann surface. In the first article the authors generalize the notion of Ahlfors function to given boundary data and in the second article the authors solve a nonlinear boundary value problem for solutions of a quasilinear Cauchy-Riemann equation on R.
The author constructs a new Hamiltonian structure of the Maxwell-Bloch equations. This system describes a continuous chain of interacting C. Neumann oscillators on the 3-sphere and the interaction is of magnetic type. Configuration space of the system is the loop group over SU(2). The author constructs a new, simpler Hamiltonian structure of the Maxwell-Bloch equations.