[...]... function that maps il on a Riemann surface with branch points of order 2 over all vertices in a net of equilateral triangles 16 CONFORMAL INVARIANTS: TOPICS IN GEOMETRIC FUNCTION THEORY 1-7 THE POINCARE METRIC OF A REGION The hyperbolic metric of a disk Izl . Conformal invariants: topics in geometric function theory I Lars V. Ahlfors. p. cm. Originally published: New York: McGraw-Hill, 1973, in series: McGraw-Hill series in higher. in more special- ized directions. ~lost conformal invariants can be described in terms of extremal properties. Conformal invariants and extremal problems are therefore intimately linked. the stronger inequality I zf"(z) - 21z12 I < 21z1 (1-9) f'(z) 1 - Izl2 - 1 - Izl2 is also in force. 6 CONFORMAL INVARIANTS: TOPICS IN GEOMETRIC FUNCTION THEORY Suppose