A General Conformal Geometric Reflection Principle
نویسنده
چکیده
We prove a generalization of the Schwarz–Carathéodory reflection principle for analytic maps f from the unit disk into arbitrary Riemann surfaces equipped with a complete real analytic conformal Riemannian metric λ(w) |dw|. This yields a necessary and sufficient condition for f to have an analytic continuation in terms of the pullback of the metric λ(w) |dw| under the map f .
منابع مشابه
Estimating Motors from a Variety of Geometric Data in 3D Conformal Geometric Algebra
The motion rotors, or motors, are used to model Euclidean motion in 3D conformal geometric algebra. In this chapter we present a technique for estimating the motor which best transforms one set of noisy geometric objects onto another. The technique reduces to an eigenrotator problem and has some advantages over matrix formulations. It allows motors to be estimated from a variety of geometric da...
متن کاملGeometric operations implemented by conformal geometric algebra neural nodes
Geometric algebra is an optimal frame work for calculating with vectors. The geometric algebra of a space includes elements that represent all the its subspaces (lines, planes, volumes, ...). Conformal geometric algebra expands this approach to elementary representations of arbitrary points, point pairs, lines, circles, planes and spheres. Apart from including curved objects, conformal geometri...
متن کاملUsing the Geometric Model to Explain the Longitudinal and Cross–Sectional Reflection Behaviors of Acrylic yarns
In the present work the reflection behavior and the color appearance of acrylic yarns, as pile yarns used in carpet and pilled fabrics, are considered along their lengths as well as their cross- sections. Differences between longitudinal and cross-sectional reflection behaviors of yarns are measured in different yarn densities and hues and explained by the geometric model. The results of experi...
متن کاملUsing the Geometric Model to Explain the Longitudinal and Cross–Sectional Reflection Behaviors of Acrylic yarns
In the present work the reflection behavior and the color appearance of acrylic yarns, as pile yarns used in carpet and pilled fabrics, are considered along their lengths as well as their cross- sections. Differences between longitudinal and cross-sectional reflection behaviors of yarns are measured in different yarn densities and hues and explained by the geometric model. The results of experi...
متن کاملOptimal Monotonicity of L Integral of Conformal Invariant Green Function
Abstract. Both analytic and geometric forms of an optimal monotone principle for Lp-integral of the Green function of a simply-connected planar domain Ω with rectifiable simple curve as boundary are established through a sharp one-dimensional power integral estimate of Riemann-Stieltjes type and the Huber analytic and geometric isoperimetric inequalities under finiteness of the positive part of...
متن کامل