Publication Date:
2016-12-01
Description:
It is classically known that the only entire zero-mean curvature graphs in the Euclidean 3-space are planes, by Bernstein's theorem. A surface in Lorentz–Minkowski 3-space R13 is called of mixed type if it changes causal type from space-like to time-like. In R13 , Osamu Kobayashi found two entire zero-mean curvature graphs of mixed type that are not planes. As far as the authors know, these two examples were the only known examples of entire zero-mean curvature graphs of mixed type without singularities. In this paper, we construct several families of real analytic entire zero-mean curvature graphs of mixed type in Lorentz–Minkowski 3-space. The entire graphs mentioned above lie in one of these classes.
Print ISSN:
0033-5606
Electronic ISSN:
1464-3847
Topics:
Mathematics
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