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Transactions of the American Mathematical Society

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

 
 

 

Examples of holomorphic functions vanishing to infinite order at the boundary


Author: Jonas Hirsch
Journal: Trans. Amer. Math. Soc. 370 (2018), 4249-4271
MSC (2010): Primary 35J67; Secondary 49Q20
DOI: https://doi.org/10.1090/tran/7192
Published electronically: February 19, 2018
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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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Jonas Hirsch
Affiliation: Mathematical Analysis, Modelling, and Applications, Scuola Internazionale Superiore di Studi Avanzati, via Bonomea, 265, 34136 Trieste, Italy

DOI: https://doi.org/10.1090/tran/7192
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
Article copyright: © Copyright 2018 American Mathematical Society

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