  Space-like maximal surfaces and time-like minimal surfaces in
Lorentz-Minkowski3-space are both characterized as zero mean curvature
surfaces. We are interested in the case where the zero mean curvature surface
changes type from space-like to time-like at a given non-degenerate null curve.
We consider this phenomenon and its interesting connection to 2-dimensional
fluid mechanics in this expository article.

Differential Geometry