Quasiconformal Mappings And Teichmullers Theorem

Cover Quasiconformal Mappings And Teichmullers Theorem
Quasiconformal Mappings And Teichmullers Theorem
Lipman Bers
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Td. I' P'jal. A h|i. Y ^2.
V has arbitrarily small compact support in S -C^, . More precisely, i\'e assume that v;e are given a and b, 0 belonging to c{>dz'^ at p and setting v(J^(p)) = n(^), we see that the re- lation to be proved becomes \ I \ rM+r, y)d'i\dE, dr^= 2a H n{^, ^)d^d''i . - CO l-a j - CO Its validity is, therefore, obvious.
12, Uniqueness proof VJe are now in a position to prove Theorem I, A) Let S jbe a c lose d Riemann surface of genus g > 1 . If f : S— > S is a c onf orma l h
...ome omorph ism homo top ic to the identity, then f _ls the ide ntity .
This classical statement follows at once from the consi- derations of §6, Set S = U/Cr and let w : U — -^ U be the horaeomorphisra inducing f. If f is conformal, vj must be con- formal, that is an element of H, If f is homotopic to the identity, w induces the identity isomorphism on G.


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