We study Christoffel and Darboux transforms of discrete isothermic nets in 4-dimensional Euclidean space: definitions and basic properties are derived. Analogies with the smooth case are discussed and a definition for discrete Ribaucour congruences is given. Surfaces of constant mean curvature are special among all isothermic surfaces: they can be characterized by the fact that their parallel c...

We propose a new algorithm for computing the Riemann mapping of the unit disk to a polygon, also known as the Schwarz–Christoffel transformation. The new algorithm, CRDT (for cross-ratios of the Delaunay triangulation), is based on cross-ratios of the prevertices, and also on cross-ratios of quadrilaterals in a Delaunay triangulation of the polygon. The CRDT algorithm produces an accurate repre...

A mesh M with planar faces is called an edge offset (EO) mesh if there exists a combinatorially equivalent mesh M d such that corresponding edges of M and M d lie on parallel lines of constant distance d. The edges emanating from a vertex of M lie on a right circular cone. Viewing M as set of these vertex cones, we show that the image of M under any Laguerre transformation is again an EO mesh. ...

We obtain an extension of the Christoffel–Darboux formula for matrix orthogonal polynomials with a generalized Hankel symmetry, including the Adler-van Moerbeke generalized orthogonal polynomials.

We prove that the correlations functions, generated by the determinantal process of the Christoffel-Darboux kernel of an arbitrary order 2 ODE, do satisfy loop equations.

It is helpful to have available systematic ways to find a variety useful conformal mappings. Our text treats one such method: bilinear transformations. Here we study a second: Schwarz-Christoffel transformations. These are discussed in many references; I recommend particularly [1], a lovely book on complex variable theory which has a decided applied slant. The Schwarz-Christoffel transformation...

A review of the uses of the CD kernel in the spectral theory of orthogonal polynomials, concentrating on recent results.

We give a method based on an idea of O. Veblen which gives explicit formulas for the covariant derivatives of natural objects in terms of the Christooel symbols of a symmetric Ehresmann "-connection.

Floryan, J.M. and C. Zemach, Schwarz-Christoffel methods for conformal mapping of regions with a periodic boundary, Journal of Computational and Applied Mathematics 46 (1993) 77-102. Numerical conformal mapping methods for regions with a periodic boundary have been developed. These methods are based on the generalized Schwarz-Christoffel equation and can deal with boundary curves of arbitrary f...