A class of discriminant varieties in the conformal 3-sphere.
A covering theorem for odd typically-real functions.
An Approximate Riemann Mapping Theorem in Cn.
Covering of radial segments for domains bounded by -circles.
Covering Theorems for Univalent Functions.
Hyperbolically convex functions
We investigate univalent holomorphic functions f defined on the unit disk 𝔻 such that f(𝔻) is a hyperbolically convex subset of 𝔻; there are a number of analogies with the classical theory of (euclidean) convex univalent functions. A subregion Ω of 𝔻 is called hyperbolically convex (relative to hyperbolic geometry on 𝔻) if for all points a,b in Ω the arc of the hyperbolic geodesic in 𝔻 connecting a and b (the arc of the circle joining a and b which is orthogonal to the unit circle) lies in...
Inverse images of function sectors in the weighted Bergman space.
J. E. McMillan's Area theorem
Mapping properties of a class of univalent functions with pre-assigned zero and pole
Obtainment of the norm in Bergman spaces.
On boundary elements of the fourth kind
On definitions of the pluricomplex Green function
We give several definitions of the pluricomplex Green function and show their equivalence.
On starlikeness of certain integral transforms
Let A denote the class of normalized analytic functions in the unit disc U = z: |z| < 1. The author obtains fixed values of δ and ϱ (δ ≈ 0.308390864..., ϱ ≈ 0.0903572...) such that the integral transforms F and G defined by and are starlike (univalent) in U, whenever f ∈ A and g ∈ A satisfy Ref’(z) > -δ and Re g’(z) > -ϱ respectively in U.
On the Residuum of Concave Univalent Functions
2000 Mathematics Subject Classification: 30C25, 30C45.Let D denote the open unit disc and f:D→[`C] be meromorphic and injective in D. We further assume that f has a simple pole at the point p О (0,1) and is normalized by f(0) = 0 and f′(0) = 1. In particular, we are concerned with f that map D onto a domain whose complement with respect to [`C] is convex. Because of the shape of f(D) these functions will be called concave univalent functions with pole p and the family of these functions is denoted...
Radial segments and conformal mapping of an annulus onto domains bounded by a circle and a k-circle
Let f(z) be a conformal mapping of an annulus A(R) = 1 < |z| < R and let f(A(R)) be a ring domain bounded by a circle and a k-circle. If R(φ) = w : arg w = φ, and l(φ) - 1 is the linear measure of f(A(R)) ∩ R(φ), then we determine the sharp lower bound of for fixed and
Rigidity of infinite disk patterns.
Schwarz's lemma for circle packings.
Sharp estimates for hyperbolic metrics and covering theorems of Landau type.
The angular distribution of mass by weighted Bergman functions.
The Bergman and Schiffer transforms on weighted norm spaces