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Is There a Teichmüller Principle in Higher Dimensions?

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Geometric Function Theory in Higher Dimension

Part of the book series: Springer INdAM Series ((SINDAMS,volume 26))

Abstract

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.

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Notes

  1. 1.

    Ich vermute, die Gesamtheit dieser Ungleichungen liefere eine vollständige Lösung des Bieberbachschen Koeffizientenproblems [41, p. 363].

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Authors and Affiliations

  1. Department of Mathematics, University of Würzburg, Würzburg, Germany

    Oliver Roth

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  1. Dipartimento di Matematica, Università di Roma Tor Vergata, Rome, Italy

    Filippo Bracci

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Roth, O. (2017). Is There a Teichmüller Principle in Higher Dimensions?. In: Bracci, F. (eds) Geometric Function Theory in Higher Dimension. Springer INdAM Series, vol 26. Springer, Cham. https://doi.org/10.1007/978-3-319-73126-1_7

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