By Perrine C. D.
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Extra resources for An Apparent Dependence of the Apex and Velocity of Solar Motion, as Determined from Radial Velocitie
To every ~ E M(G,Z) a unique normalized there corresponds (Ahlfors-Bers (fixing 0,1,~) ~-conformal ) automorphism of denoted by w ~. 1. A Beltrami coefficient is called trivial if it satisfies followin$ conditions: a) ~ogo(w~)-i : g, all g ~ G, one (hence both) W E M(G,Z) of the 5O b) w~(z) = z, all z E A, the limit set of G. 2. of the following fixes each component elementary A__nnorientation preserving maps every component o_~f the complement of topological automorphism o f ~ of its fixed point set onto itself.
X %(Gr,~r). The first isomorphism is trivial. 2. Let D be an open subset of ~ and f ~ topological homeomorphism of~ fI~kD = id. coefficient that is quasiconformal Then f i_~s q u a s i c o n f o r m a l is supported o__n_nD and such that and its Beltrami in D. 8 leads (Maskit to the following ). quasiconformal §3° (conformal) REDUCTION universal Then f is the A automorphism F of C all g £ G. Further, if f i__ss. of Z. Let h : U ~ ~ be a holo- covering map. Let F be the F u c h s i a n model of G over 4; that is, the group of conformal ¥ of U such that there is a X(Y) We then have an exact sequence [i} > H in~ > F X with H (the covering group) of finite Riemann type F i_~s TO THE F U C H S I A N CASE Let A be a component morphic automor- all g 6 G.
It acts properly 60 discontinuously o_n_n~(G,E), and ~(G,E) is thus a normal complex space. The group Mod(G,Z) is induced by quasiconformal auto- morphisms f of ~ that conjugate G into itself and fix E. There is thus a normal subgroup MOdo(G,E) of finite index in Mod (G,E) that is induced by quasiconformal automorphisms of A C that fix each E~~ = [g(Aj);g E G]. Let f be such an autoA morphism of $. For each j, there is a g~ ~ G such that fj = gjlof fixes Aj and fjGjfj I = Gj. By the introductory remarks of §6, there is an automorphism w.