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arXiv · 1509.03749

Examples of holomorphic functions vanishing to infinite order at the boundary

Jonas Hirsch
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Abstract

We present examples of holomorphic functions that vanish to in- finite 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 dis- cuss 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. 2015-09-12. Examples of holomorphic functions vanishing to infinite order at the boundary. https://arxiv.org/abs/1509.03749

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