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Zero mean curvature surfaces in Lorentz-Minkowski 3-space and 2-dimensional fluid mechanics. (English) Zbl 1320.53017

Space-like maximal surfaces and time-like minimal surfaces in Lorentz-Minkowski 3-space \(\mathbb R^3_1\) are both characterized as zero mean curvature surfaces. The authors 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. One considers this phenomenon and its interesting connection to 2-dimensional fluid mechanics in this expository article.

MSC:

53A35 Non-Euclidean differential geometry
53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
53B30 Local differential geometry of Lorentz metrics, indefinite metrics
35Q35 PDEs in connection with fluid mechanics
76G99 General aerodynamics and subsonic flows
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