The Schwarz Function and Its Applications |
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Page 82
... angle . ( See Fig . 8.10 . ) Denote the angle between the arcs by 0. If 0 , the figure is often called a horn angle . ( See Fig . 8.11 . ) Now if a transformation ƒ is analytic in a neighbor- hood of P , and f ' ( P ) property of ...
... angle . ( See Fig . 8.10 . ) Denote the angle between the arcs by 0. If 0 , the figure is often called a horn angle . ( See Fig . 8.11 . ) Now if a transformation ƒ is analytic in a neighbor- hood of P , and f ' ( P ) property of ...
Page 83
Philip J. Davis. لا P FIG . 8.11 - Horn angle between two analytic arcs is a conformal invariant . But it turns out that if two angles have the same 0 , they are not necessarily equivalent conformally . For example , one can find two ...
Philip J. Davis. لا P FIG . 8.11 - Horn angle between two analytic arcs is a conformal invariant . But it turns out that if two angles have the same 0 , they are not necessarily equivalent conformally . For example , one can find two ...
Page 85
... horn angles be conformally equivalent . If the order of contact between P and Q is higher , a similar argument works and it can be shown that every horn angle has one and only one higher conformal invariant . We turn our attention next ...
... horn angles be conformally equivalent . If the order of contact between P and Q is higher , a similar argument works and it can be shown that every horn angle has one and only one higher conformal invariant . We turn our attention next ...
Contents
CHAPTER PAGE 1 Prologue 15739 | 1 |
Conjugate Coordinates in the Plane | 2 |
Elementary Geometrical Facts | 3 |
Copyright | |
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A₁ algebra analytic arc analytic continuation analytic curve analytic function anti-analytic assume b₁ bilinear bisector Cauchy Chapter clinant coefficients complex number complex variables conformal invariant conformal mapping conjugate coordinates convergence curvilinear angle defined derivative designate differential equations dxdy Example F₂ fixed point follows formal power series formula func Function for f functional composition functional equation geometry harmonic function Hence horn angle identity integral interior intersect inverse inversive geometry iteration LEMMA linear Math mathematics matrix meromorphic Möbius Möbius transformation neighborhood nine-point circle obtain orthocenter orthogonal plane polynomial problem Proof real axis schlicht Schroeder Function Schwarz Function S(z Schwarzian reflection simply connected simply connected region single-valued solution spiral straight line Suppose symmetric with respect tangent theorem theory tion transformation triangle unit circle write x-axis z₁ дв