x INTRODUCTIO N Kenig woul d lik e t o than k T . Tor o fo r he r fundamenta l contributio n t o thei r joint wor k an d D . Jeriso n fo r man y conversation s o n th e subjec t throughou t th e years. Keni g woul d als o lik e t o than k Lui s Caffarell i an d Gu y Davi d fo r usefu l discussions, an d G . David fo r hi s role in their joint wor k in the higher co-dimensio n case o f the geometri c measur e theor y results . We ar e indebte d t o Joa n Carmona , Christia n Pommerenke , an d Joa n Verder a for discussing with us many of the two-dimensional results . I t i s a pleasure to than k Chaim Goodman-Straus s fo r producin g th e picture s i n th e book , an d Christin e Thiverge at the American Mathematical Societ y for her assistance with this project . Last bu t no t least , th e author s wis h to than k th e Nationa l Scienc e Foundatio n and th e Universit y o f Arkansa s fo r sponsorin g th e 200 0 Arkansa s Sprin g Lecture s Series.
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