Value Distribution Theory for Meromorphic Maps

  • Authors
  • Wilhelm Stoll

Table of contents

  1. Front Matter
    Pages I-XI
  2. Wilhelm Stoll
    Pages 1-91
  3. Wilhelm Stoll
    Pages 92-114
  4. Wilhelm Stoll
    Pages 115-133
  5. Wilhelm Stoll
    Pages 134-150
  6. Wilhelm Stoll
    Pages 151-162
  7. Wilhelm Stoll
    Pages 163-190
  8. Wilhelm Stoll
    Pages 191-215
  9. Wilhelm Stoll
    Pages 216-244
  10. Wilhelm Stoll
    Pages 245-274
  11. Wilhelm Stoll
    Pages 275-309
  12. Wilhelm Stoll
    Pages 310-316
  13. Wilhelm Stoll
    Pages 317-333
  14. Wilhelm Stoll
    Pages 334-343
  15. Back Matter
    Pages 344-347

About this book

Introduction

Value distribution theory studies the behavior of mermorphic maps. Let f: M - N be a merom orphic map between complex manifolds. A target family CI ~ (Ea1aEA of analytic subsets Ea of N is given where A is a connected. compact complex manifold. The behavior of the inverse 1 family ["'(CI) = (f- {E )laEA is investigated. A substantial theory has been a created by many contributors. Usually the targets Ea stay fixed. However we can consider a finite set IJ of meromorphic maps g : M - A and study the incidence f{z) E Eg(z) for z E M and some g E IJ. Here we investigate this situation: M is a parabolic manifold of dimension m and N = lP n is the n-dimensional projective space. The family of hyperplanes in lP n is the target family parameterized by the dual projective space lP* We obtain a Nevanlinna theory consisting of several n First Main Theorems. Second Main Theorems and Defect Relations and extend recent work by B. Shiffman and by S. Mori. We use the Ahlfors-Weyl theory modified by the curvature method of Cowen and Griffiths. The Introduction consists of two parts. In Part A. we sketch the theory for fixed targets to provide background for those who are familar with complex analysis but are not acquainted with value distribution theory.

Keywords

Complex analysis Meromorphic function Nevanlinna theory map

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-663-05292-0
  • Copyright Information Springer Fachmedien Wiesbaden GmbH 1985
  • Publisher Name Vieweg+Teubner Verlag, Wiesbaden
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-663-05294-4
  • Online ISBN 978-3-663-05292-0
  • About this book