Value Distribution Theory And Related Topics (advances In Complex Analysis And Its Applications)

VALUE DISTRIBUTION THEORY AND RELATED TOPICS Advances in Complex Analysis and Its Applications Volume 3 Series Editor: C.C. Yang The Hong Kong University of Science& Technology, Hong Kong Advisory Board: Walter Bergweiler Keil University, Germany George Csordas University of Hawaii, U.S.A. Paul Gauthier University of Montreal, Canada Phillip Griffiths Princeton, U.S.A. Irwin Kra State University of New York, U.S.A. Armen G. Sergeev Steklov Institute of Mathematics, Russia Wolfgang Tutschke University of Graz, Austria VALUE DISTRIBUTION THEORY AND RELATED TOPICS edited by G. Barsegian National Academy of Sciences of Armenia Yerevan, Armenia I. Laine University of Joensuu Joensuu, Finland C.C. Yang Hong Kong University of Science and Technology Hong Kong, China KLUWER ACADEMIC PUBLISHERS NEW YORK, BOSTON, DORDRECHT, LONDON, MOSCOW eBook ISBN: Print ISBN: 1-4020-7951-6 1-4020-7950-8 ©2004 Kluwer Academic Publishers New York, Boston, Dordrecht, London, Moscow Print ©2004 Kluwer Academic Publishers Boston All rights reserved No part of this eBook may be reproduced or transmitted in any form or by any means, electronic, mechanical, recording, or otherwise, without written consent from the Publisher Created in the United States of America Visit Kluwer Online at: and Kluwer's eBookstore at: http://kluweronline.com http://ebooks.kluweronline.com CONTENTS Preface vii Geometric value distribution theory Barsegian, G.: A new program of investigations in analysis: Gamma-lines approaches Sukiasyan, G.: On level sets of quasiconformal mappings 1 75 Classical value distribution theory Alonso, A., Fernández, A. and Pérez, J.: On the unintegrated Nevanlinna fundamental inequality for meromorphic functions of slow growth 93 Barsegian, G. and Yang, C.-C.: On some new concept of exceptional values 105 Ciechanowicz, E. and Marchenko, I.: Maximum modulus points, deviations and spreads of meromorphic functions 117 Craven, T. and Csordas, G.: Composition theorems, multiplier sequences and complex zero decreasing sequences Korhonen, R.: Nevanlinna theory in an annulus 131 167 Marchenko, I. and Nikolenko, I.: On strong asymptotic tracts of functions holomorphic in a disk 181 Complex differential and functional equations Barsegian, G., Sarkisian, A. and Yang, C.-C.: A new trend in complex differential equations: quasimeromorphic solutions 189 Ha, H.K. and Yang, C.-C.: On the functional equation 201 He, Y.: Value distribution of the higher order analogues of the first Painlevé equation 209 Yang, C.-C. and Li, P.: Some further results on the functional equation 219 vi Several variables theory Aihara, Y.: Recent topics in uniqueness problem for meromorphic mappings 233 Berenstein, C. and Li, B.Q.: On interpolation problems in 265 Hu, P.-C. and Yang, C.-C.: Jet bundles and its applications in value distribution of holomorphic mappings Tu, Z.-H.: Normal families of meromorphic mappings of several complex variables into the complex projective space 281 321 PREFACE The Nevanlinna theory of value distribution of meromorphic functions, one of the milestones of complex analysis during the last century, was created to extend the classical results concerning the distribution of of entire functions to the more general setting of meromorphic functions. Later on, a similar reasoning has been applied to algebroid functions, subharmonic functions and meromorphic functions on Riemann surfaces as well as to analytic functions of several complex variables, holomorphic and meromorphic mappings and to the theory of minimal