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