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.


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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