Improvement of the Bernstein-type theorem for space-like zero mean curvature graphs in Lorentz-Minkowski space using fluid mechanical duality
Improvement of the Bernstein-type theorem for space-like zero mean curvature graphs in Lorentz-Minkowski space using fluid mechanical duality
复制标题
利用流体力学对偶性改进 Lorentz-Minkowski 空间中类空间零均曲率图的 Bernstein 型定理
DOI：
10.1090/bproc/44
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Yamada K.
中科院分区：
文献类型：
--
作者：
Akamine S.;Umehara M.;Yamada K.
Calabi的Bernstein型定理证明了Lorentz-Minkowski空间中的零平均曲率整图是类空平面。利用三维欧氏空间中极小曲面与Lorentz-Minkowski空间中极大曲面之间的流体力学对偶性，给出了Bernstein型定理的一个改进.更精确地说，我们证明了一个不允许类时点存在的零平均曲率整图，即一个只包含类空点和类光点的图是一个平面。引用
Calabi’s Bernstein-type theorem asserts that a zero mean curvature entire graph in Lorentz-Minkowski spacewhich admits only space-like points is a space-like plane. Using the fluid mechanical duality between minimal surfaces in Euclidean 3-spaceand maximal surfaces in Lorentz-Minkowski space, we give an improvement of this Bernstein-type theorem. More precisely, we show that a zero mean curvature entire graph inwhich does not admit time-like pointsnamely, a graph consists of only space-like and light-like pointsis a plane. References