Shabat polynomials and harmonic measure

  • Philippe BianeEmail author
Part of the Lecture Notes in Mathematics book series (LNM, volume 1979)


This note is inspired by [BZ], which describes the true shape of a tree. Each planar tree (remember that a planar tree is a tree in which, for each vertex, the adjacent edges are cyclically ordered) has a distinguished embedding in the complex plane (up to similitude).


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  1. [BZ].
    Bétréma, J., Zvonkin, A.: La vraie forme d'un arbre. TAPSOFT '93: theory and practice of software development (Orsay, 1993), 599–612, Lecture Notes in Comput. Sci., 668, Springer, Berlin, 1993. 05C05.Google Scholar
  2. [D].
    Doob, J.L.: Classical potential theory and its probabilistic counterpart. Grundlehren der Mathematischen Wissenschaften, 262. Springer-Verlag, New York, 1984.Google Scholar
  3. [LZ].
    Lando, S., Zvonkin, A.: Graphs on surfaces and their applications, Encyclopedia of Mathematical Sciences, Low dimensional topology, II. Springer-Verlag, berlin, Heidelberg, 2004.Google Scholar
  4. [MR].
    Marshall, D.E.; Rohde, S.: The Löwner differential equation and slit mappings. J. Amer. Math. Soc. 18 (2005), no. 4, 763–778.MathSciNetzbMATHCrossRefGoogle Scholar
  5. [R].
    Rudin, W.: Real and complex analysis. Third edition. McGraw-Hill Book Co., New York, 1987.zbMATHGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.CNRS Laboratoire d’Informatique Institut Gaspard Monge Université Paris-EstChamps-sur-Marnecedex 2

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