The Schwarz Lemma: Rigidity and Dynamics

  • Mark ElinEmail author
  • Fiana Jacobzon
  • Marina Levenshtein
  • David Shoikhet
Part of the Trends in Mathematics book series (TM)


The Schwarz Lemma has given impetus to developments in several areas of complex analysis and mathematics in general. We survey some investigations related to its three parts (invariance, rigidity, and distortion) that began early in the twentieth century and are still being carried out. We consider only functions analytic in the unit disk. Special attention is devoted to the Boundary Schwarz Lemma and to applications of the Schwarz–Pick Lemma and the Boundary Schwarz Lemma to modern rigidity theory and complex dynamics.


Schwarz Lemma Schwarz-Pick Inequality Denjoy Wolff Point Holomorphic Self-mapping Boundary Denjoy Wolff Point 
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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© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Mark Elin
    • 1
    Email author
  • Fiana Jacobzon
    • 1
  • Marina Levenshtein
    • 1
  • David Shoikhet
    • 1
  1. 1.Department of MathematicsORT Braude CollegeKarmielIsrael

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