Schwarz Reflection Geometry I: Continuous Iteration of Reflection
نویسندگان
چکیده
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.
منابع مشابه
Schwarz 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 کاملSchwarz-christoffel Mapping of Multiply Connected Domains
A Schwarz-Christoffel mapping formula is established for polygonal domains of finite connectivity m ≥ 2 thereby extending the results of Christoffel (1867) and Schwarz (1869) for m = 1 and Komatu (1945), m = 2. A formula for f, the conformal map of the exterior of m bounded disks to the exterior of m bounded, disjoint polygons, is derived. The derivation characterizes the global preSchwarzian f...
متن کاملEffects of Reflection on Clinical Learning of Medical Students
Introduction: Reflection is considered as a critical characteristic in professional competitions. Despite propagation of reflection as an important educational issue and existence of several helpful patterns, instructions conducted by teachers to explaining and expanding of it, are very little. Studies related to this topic were mainly performed in the field of nursing. Therefore, we decided to...
متن کاملA Direct Proof for Riemann Hypothesis Based on Jacobi Functional Equation and Schwarz Reflection Principle
Using the properties of theta-series and Schwarz reflection principle, a proof for Riemann hypothesis (RH) is directly presented and the first ten nontrivial zeros are easily obtained. From now on RH becomes Riemann Theorem (RT) and all its equivalent results and the consequences assuming RH are true.
متن کاملThe Reflection of the Hymn of "Allah Allah" in the Tower of the Mausoleum of Sheikh Safi al-Din Ardabili and its Position in the Safavid Sufism
After the death of Sheikh Safi al-Din Ardabili in 735 AH. / 1335 AD., his mausoleum was developed by his son and his successor, Sheikh Sadr al-Din Musa, and later expanded, especially during the reign of Safavid Shah Tahmasb I and Shah Abbas I. The hymn of "Allah Allah" is the most remarkable hymns in the tower of the mausoleum of Sheikh Safi al-Din Ardabili, so that it is often referred to as ...
متن کامل