Schwarz reflection geometry I: Continuous iteration of reflection
نویسندگان
چکیده
منابع مشابه
Schwarz Reflection Geometry I: Continuous Iteration of Reflection
Differential equations are derived for a continous limit of iterated Schwarzian reflection of analytic curves, and solutions are interpreted as geodesics in an infinite-dimensional symmetric space geometry.
متن کاملA Constructive Schwarz Reflection Principle
We prove a constructive version of the Schwarz reflection principle. Our proof techniques are in line with Bishop’s development of constructive analysis. The principle we prove enables us to reflect analytic functions in the real line, given that the imaginary part of the function converges to zero near the real line in a uniform fashion. This form of convergence to zero is classically equivale...
متن کاملThe Geometry of Reflection Groups
or perhaps with the face of our mother or father. We quickly learn to identify the axis of symmetry and know intuitively that an object is symmetric if it “the same” on both sides of this axis. In mathematics symmetry is abundant and takes many forms. Symmetry like that of the butterfly or a face is referred to as reflexive symmetry. Any line in the plane determines a unique symmetry which refl...
متن کاملContinuous symplectic reflection algebras
The theory of PBW properties of quadratic algebras, to which this paper aims to be a modest contribution, originates from the pioneering work of Drinfeld (see [Dr1]). In particular, as we learned after publication of [EG] (to the embarrassment of two of us!), symplectic reflection algebras and even more general reflection algebras considered in Section 3.6 below, as well as PBW theorems for the...
متن کاملSchwarz Reflection Geometry II: Local and Global Behavior of the Exponential Map
A local normal form is obtained for geodesics in the space Λ = {Γ} of analytic Jordan curves in the extended complex plane with symmetric space multiplication Γ1 · Γ2 defined by Schwarzian reflection of Γ2 in Γ1. Local geometric features of (Λ, ·) will be seen to reflect primarily the structure of the Witt algebra, while issues of global behavior of the exponential map will be viewed in the con...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematische Zeitschrift
سال: 2003
ISSN: 0025-5874,1432-1823
DOI: 10.1007/s00209-003-0523-1