ZERO MEAN CURVATURE SURFACES IN LORENTZ-MINKOWSKI 3-SPACE AND 2-DIMENSIONAL FLUID MECHANICS

Space-like maximal surfaces and time-like minimal surfaces in Lorentz-Minkowski 3-space R³₁ 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.