English

Examples of holomorphic functions vanishing to infinite order at the boundary

Analysis of PDEs 2017-12-21 v3

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.

Keywords

Cite

@article{arxiv.1509.03749,
  title  = {Examples of holomorphic functions vanishing to infinite order at the boundary},
  author = {Jonas Hirsch},
  journal= {arXiv preprint arXiv:1509.03749},
  year   = {2017}
}

Comments

21 pages