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Chebyshev and Robin constants on algebraic curves

Volume 115 / 2015

Jesse Hart, Sione Ma`u Annales Polonici Mathematici 115 (2015), 101-121 MSC: Primary 32U35; Secondary 32C25. DOI: 10.4064/ap115-2-1

Abstract

We define directional Robin constants associated to a compact subset of an algebraic curve. We show that these constants satisfy an upper envelope formula given by polynomials. We use this formula to relate the directional Robin constants of the set to its directional Chebyshev constants. These constants can be used to characterize algebraic curves on which the Siciak–Zaharjuta extremal function is harmonic.

Authors

  • Jesse HartDepartment of Mathematics
    University of Auckland
    Auckland, New Zealand
    e-mail
  • Sione Ma`uDepartment of Mathematics
    University of Auckland
    Auckland, New Zealand
    e-mail

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