Related papers: Schwarz-Christoffel: piliero en rivero (a pillar o…
An iterative numerical method to compute the conformal mapping in the context of propagating water waves over uneven topographies is investigated. The map flattens the fluid domain onto a canonical strip in which computations are performed.…
In this paper we construct an affine model of a Riemann surface with a flat Riemannian metric associated to a Schwarz-Christoffel mapping of the upper half plane onto a rational triangle. We explain the relation between the geodesics on…
In the article we consider the composite conformal map which maps annulus to infinite region with symmetric hole and nearly circular hole. It is shown that such transformation is good if the distance between centers of holes are large or…
We show that the computational complexity of Riemann mappings can be bounded by the complexity needed to compute conformal mappings locally at boundary points. As a consequence we get first formally proven upper bounds for…
A generalization of the Schwarz-Christoffel mapping to multiply connected polygonal domains is obtained by making a combined use of two preimage domains, namely, a rectilinear slit domain and a bounded circular domain. The conformal mapping…
The conformal mapping problem for the section of a channel filled with porous material under a rectangular dam onto the upper half-plane is considered. Similar problems arise in computing of fluid flow in hydraulic structures. As a solution…
A novel method rooted in the classical Schwarz-Christoffel transformation from the disk is introduced, which allows for fast and accurate solution of potential field problems in possibly inhomogeneous and multiply connected domains: this is…
Consider the straightening phi of a Beltrami form that is constant on a square, with the corresponding ellipses having a vertical major axis, and null outside. A generalized Schwarz-Christoffel formula is used to express the inverse of phi.…
We extend previous work on Schwarz-Chrsitoffel mappings, including the special cases when the image is a convex polygon or its complement. We center our analysis on the relationship between the pre-Schwrazian of such mappings and Blaschke…
Suppose that $M$ is a K\"ahler manifold with a pole such that its holomorphic sectional curvature is bounded from below by a constant and its radial sectional curvature is also bounded from below. Suppose that $N$ is a strongly pseudoconvex…
In this article, we consider the Christoffel transformations for skew-orthogonal polynomials and partial-skew-orthogonal polynomials. We demonstrate that the Christoffel transformations can act as spectral problems for discrete integrable…
We study the interior and exterior moduli of polygonal quadrilaterals. The main result is a formula for a conformal mapping of the upper half plane onto the exterior of a convex polygonal quadrilateral. We prove this by a careful analysis…
We introduce and study the notion of a locally proper map between topological spaces. We show that fundamental constructions of sheaf theory, more precisely proper base change, projection formula, and Verdier duality, can be extended from…
The double exponential formula, or the DE formula, is a high-precision integration formula using a change of variables called a DE transformation; whereas there is a disadvantage that it is sensitive to singularities of an integrand near…
Deformations of compact Riemann surfaces are considered using a \v{C}ech cohomology sliding overlaps approach. Cocycles are calculated for conformal cutting and regluing deformations at zeros of Abelian differentials. A second order…
We introduce an elementary transformation called flips on tilings by squares and triangles and conjecture that it connects any two tilings of the same region of the Euclidean plane.
Quasiconformal maps in the plane are orientation preserving homeomorphisms that satisfy certain distortion inequalities; infinitesimally, they map circles to ellipses of bounded eccentricity. Such maps have many useful geometric distortion…
Invertible compositions of one-dimensional maps are studied which are assumed to include maps with non-positive Schwarzian derivative and others whose sum of distortions is bounded. If the assumptions of the Koebe principle hold, we show…
A conformal map from a Riemann surface to the Euclidean four-space is explained in terms of its twistor lift. A local factorization of a differential of a conformal map is obtained. As an application, the factorization of a differential…
A spatial network is constructed on a two dimensional space where the nodes are geometrical points located at randomly distributed positions which are labeled sequentially in increasing order of one of their co-ordinates. Starting with $N$…