Bernstein-type theorem for zero mean curvature hypersurfaces without time-like points in Lorentz-Minkowski space
Bernstein-type theorem for zero mean curvature hypersurfaces without time-like points in Lorentz-Minkowski space
复制标题
Lorentz-Minkowski 空间中无类时点的零平均曲率超曲面的 Bernstein 型定理
DOI：
10.1007/s00574-020-00196-8
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
Kotaro Yamada
中科院分区：
文献类型：
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作者：
Shintaro Akamine;Atsufumi Honda;Masaaki Umehara;Kotaro Yamada
Calabi和Cheng-Yau的bernstein型定理断言，在洛伦兹-闵可夫斯基空间$${{\varvec{R}}_{1}^{n+1}}$$中只允许类空间点的整个零平均曲率图是一个超平面。最近，第三和第四作者证明了超曲面在简并类光点处的一条直线定理。利用这一点，我们对bernstein型定理进行了改进，并证明了在$${\varvec{R}}^{n+1}_1$$中仅由类空点或类光点组成的整个零平均曲率图是一个超平面。这是第一，第三和第四作者之前的结果的概括。
Calabi and Cheng-Yau’s Bernstein-type theorem asserts thatan entire zero mean curvature graph in Lorentz–Minkowski-space$${{\varvec{R}}_{1}^{n+1}}$$which admits only space-like points is a hyperplane. Recently, the third and fourth authors proved a line theorem for hypersurfaces at their degenerate light-like points. Using this, we give an improvement of the Bernstein-type theorem, and we show thatan entire zero mean curvature graph in$${\varvec{R}}^{n+1}_1$$consisting only of space-like or light-like points is a hyperplane. This is a generalization of the first, third and fourth authors’ previous result for.