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Ramified integrals

  • Anton Savin
  • Boris Sternin
Chapter
  • 869 Downloads
Part of the Frontiers in Mathematics book series (FM)

Abstract

We consider the notion of integrals depending on a parameter. Unexpectedly, this notion turns out to be quite nontrivial in complex analysis: even in the situation, when the integrand is a single-valued form, the integral is a ramified function as a rule. For this reason, parametric integrals in complex analysis are also called ramified integrals. The aim of this chapter is to describe this phenomenon in examples and then present the general theory of such integrals.

Keywords

Riemannian Surface Analytic Continuation Homology Class Holomorphic Form Compact Complex Manifold 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Anton Savin
    • 1
    • 2
  • Boris Sternin
    • 1
    • 2
  1. 1.Department of Applied MathematicsRUDN UniversityMoscowRussia
  2. 2.Institut für AnalysisLeibniz Universität HannoverHannoverGermany

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