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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Examples of holomorphic functions vanishing to infinite order at the boundary
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by Jonas Hirsch PDF
Trans. Amer. Math. Soc. 370 (2018), 4249-4271 Request permission

Abstract:

We present examples of holomorphic functions that vanish to infinite order at points at the boundary of their domain of definition. They give rise to examples of Dirichlet minimizing $Q$-valued functions indicating that “higher”-regularity boundary results are difficult. Furthermore we discuss some implication to branching and vanishing phenomena in the context of minimal surfaces, $Q$-valued functions, and unique continuation.
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Additional Information
  • Jonas Hirsch
  • Affiliation: Mathematical Analysis, Modelling, and Applications, Scuola Internazionale Superiore di Studi Avanzati, via Bonomea, 265, 34136 Trieste, Italy
  • Received by editor(s): June 16, 2016
  • Received by editor(s) in revised form: June 28, 2016, and November 18, 2016
  • Published electronically: February 19, 2018
  • © Copyright 2018 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 370 (2018), 4249-4271
  • MSC (2010): Primary 35J67; Secondary 49Q20
  • DOI: https://doi.org/10.1090/tran/7192
  • MathSciNet review: 3811527