Approximating singularities by a cuspidal edge on a maxface

Abstract

We give necessary and sufficient conditions on the singular Björling data to the singular Björling problem's solution has a prescribed nature of singularity. As an application, we prove that near a maxface with a particular type of singularity, there is another maxface having a cuspidal-edge. An example of a maxface having various types of singularities is also given.

arXiv commentJournal information updated. To appear in Archiv der Mathematik