It is well-known that space-like maximal surfaces and time-like minimal surfaces in Lorentz–Minkowski 3-space R31 have singularities in general. They are both characterized as zero mean curvature surfaces. We are interested in the case where the singular set consists of a light-like line, since this case has not been analyzed before. As a continuation of a previous work by the authors, we give the first example of a family of such surfaces which change type across a light-like line. As a corollary, we also obtain a family of zero mean curvature hypersurfaces in Rn+11 that change type across an (n - 1)-dimensional light-like plane.
|Number of pages||13|
|Journal||Osaka Journal of Mathematics|
|Publication status||Published - 2015|
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