Approximating singularities by a cuspidal edge on a maxface
Abstract
We give necessary and sufficient conditions on the singular Bj\"orling data to the singular Bj\"orling 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.
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