Automorphisms and Finite Inner Maps

  • Reinhold Remmert
Part of the Graduate Texts in Mathematics book series (GTM, volume 172)


The group Aut G and the semigroup Hol G, which were already studied in 8.4, are central to Sections 1 and 2. For bounded domains G, every sequence fn ∈ Hol G has a convergent subsequence (Montel); this fact has surprising consequences. For example, in H. Cartan’s theorem, one can read off from the convergence behavior of the sequence of iterates of a map f : G → G whether f is an automorphism of G. In 2.5, as an application of Cartan’s theorem, we give a homological characterization of automorphisms.


Boundary Sequence Convergent Subsequence Closed Subgroup Mapping Degree Finite Blaschke Product 
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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Reinhold Remmert
    • 1
  1. 1.Mathematisches InstitutWestfälische Wilhelms—Universität MünsterMünsterGermany

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