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Constant-mean-curvature surfaces with singularities in Minkowski 3-space. (English) Zbl 1182.53008

Summary: We investigate space-like constant-mean-curvature surfaces with singularities in Minkowski 3-space. Recently, Kokubu, Rossman, Saji, Umehara, and Yamada gave useful criteria for cuspidal edges and swallowtails. Applying their criteria, we define a new class of generalized constant-mean-curvature surface and give some examples with cuspidal edges and swallowtails.

MSC:

53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
53C43 Differential geometric aspects of harmonic maps
53B30 Local differential geometry of Lorentz metrics, indefinite metrics
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