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generalised the lemma to maps from the unit disk to other negatively curved surfaces:
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to itself, will not increase the
Poincaré distance between points. The unit disk
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287:{\displaystyle \sigma (f(z_{1}),f(z_{2}))\leq \rho (z_{1},z_{2})}
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Extension of the
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153:is ≤ −1; let
418:. You can help Knowledge (XXG) by
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480:Theorems in differential geometry
339:{\displaystyle z_{1},z_{2}\in U.}
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178:{\displaystyle f:U\rightarrow S}
27:theorem is an extension of the
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475:Theorems in complex analysis
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142:{\displaystyle \sigma }
57:to itself, or from the
414:-related article is a
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111:{\displaystyle \rho }
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48:holomorphic function
25:Schwarz–Ahlfors–Pick
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412:Riemannian geometry
33:hyperbolic geometry
381:Notices of the AMS
372:(September 1999).
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151:Gaussian curvature
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70:Gaussian curvature
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72:−1. In 1938,
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74:Lars Ahlfors
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21:mathematics
459:Categories
356:References
352:in 1973.
328:∈
253:ρ
250:≤
200:σ
170:→
137:σ
106:ρ
52:unit disk
50:from the
297:for all
189:. Then
94:). Let
88:Ahlfors
84:Schwarz
80:Theorem
149:whose
118:; let
23:, the
410:This
377:(PDF)
185:be a
122:be a
416:stub
92:Pick
42:The
31:for
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