Geometric theory of functions of a complex variable

  title={Geometric theory of functions of a complex variable},
  author={Gennadiĭ Mikhaĭlovich Goluzin},
Majorization for Starlike and Convex functions with respect to Conjugate points
The concept of majorization is now well-known after the beautiful work of MacGregor, and then followed by Campbell in his sequel of papers. In this paper, we establish the sharp majorization results
Multiple bubbles and fingers in a Hele-Shaw channel: complete set of steady solutions
Analytical solutions for both a finite assembly and a periodic array of bubbles steadily moving in a Hele-Shaw channel are presented. The particular case of multiple fingers penetrating into the
On the Riemann-Hilbert problem for the Beltrami equation
It is developed the theory of the Dirichlet problem for harmonic functions. On this basis, for the nondegenerate Beltrami equations in the quasidisks and, in particular, in the smooth domains, it is
Lempert Theorem for stronly linearly convex domains with smooth boundaries
The aim of this paper is to present a detailed and slightly modified version of the proof of the Lempert Theorem in the case of non-planar stronlgy linearly convex domains with C^2 smooth boundaries.
Mono-components for decomposition of signals
This note further carries on the study of the eigenfunction problem: Find f(t)=ρ(t)eiθ(t) such that Hf=−if, ρ(t)⩾0 and θ′(t)⩾0, a.e. where H is Hilbert transform. Functions satisfying the above
Applications of special function theory to complex analysis
For any two points a1 and a2 in an open disk Δ on the complex sphere C¯, let L be a curve separating a 1 from a2 on C¯, which splits C¯ into two complementary regions B 1 ∋ a1 and B2 ∋ a2. Let l be a
Quasiconformal mappings and periodic spectral problems in dimension two
We study spectral properties of second-order elliptic operators with periodic coefficients in dimension two. These operators act in periodic simply-connected waveguides, with either Dirichlet, or
External rays to periodic points
We prove that for every polynomial-like holomorphic mapP, ifaεK (filled-in Julia set) and the componentKaofK containinga is either a point ora is accessible along a continuous curve from the
Crossing Symmetric Spinning S-matrix Bootstrap: EFT bounds
We develop crossing symmetric dispersion relations for describing 2-2 scattering of identical external particles carrying spin. This enables us to import techniques from Geometric Function Theory and