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arXiv · 1907.00739

Space-like maximal surfaces containing entire null lines in Lorentz-Minkowski 3-space

Shintaro Akamine·Masaaki Umehara·Kotaro Yamada
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Abstract

Consider a surface $S$ immersed in the Lorentz-Minkowski 3-space $\boldsymbol R^3_1$. A complete light-like line in $\boldsymbol R^3_1$ is called an entire null line on the surface $S$ in $\boldsymbol R^3_1$ if it lies on $S$ and consists of only null points with respect to the induced metric. In this paper, we show the existence of embedded space-like maximal graphs containing entire null lines. If such a graph is defined on a convex domain in $\boldsymbol R^2$, then it must be a light-like plane. Our example is critical in the sense that it is defined on a certain non-convex domain.

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Shintaro Akamine, Masaaki Umehara, Kotaro Yamada. 2019-07-01. Space-like maximal surfaces containing entire null lines in Lorentz-Minkowski 3-space. https://arxiv.org/abs/1907.00739

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