Is There a Teichmüller Principle in Higher Dimensions?

  • Oliver RothEmail author
Part of the Springer INdAM Series book series (SINDAMS, volume 26)


The underlying theme of Teichmüller’s papers in function theory is a general principle which asserts that every extremal problem for univalent functions of one complex variable is connected with an associated quadratic differential. The purpose of this paper is to indicate a possible way of extending Teichmüller’s principle to several complex variables. This approach is based on the Loewner differential equation.


Loewner theory Extremal problems Control theory 

Mathematics Subject Classification (2000)

30C55 32H02 49K15 


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Authors and Affiliations

  1. 1.Department of MathematicsUniversity of WürzburgWürzburgGermany

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