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4 The variational formula
6 Admissible functionals
10 other sections not shown
1+e z 1+ltl analytic function arbitrary boundary arcs boundary value problem bounded functions branch point calculation coefficients Consider the variation Corollary 3.1 derivatives determined differential equation 3.2 Doctor of Philosophy double zero end conditions expansion exterior points extremal condition extremal functions finite number function defined function f(z functional derivative functional differential equation Green's function Hence inequality integrating interior variation 1.3 koebe function l+|t linear Lowner's differential equation meromorphic function n+1 n+1 necessary condition o o o o open set problem 2.1 radial slit mapping rational function real constant real parameter ReF _ ImF regular analytic relation resp satisfy the differential satisfy the side Schwarz lemma Schwarz reflection side condition f(t side conditions 1.1 sign(t-r simply connected solution Substituting theorem 1.1 unique unit circle unit disc unit periphery variation 1.4 variational formula yield the system Yk B(z,zk zero of R(w zeroes and poles