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Reflection principle for lightlike line segments on maximal surfaces
Shintaro Akamine, Hiroki Fujino
As in the case of minimal surfaces in the Euclidean 3-space, the reflection principle for maximal surfaces in the Lorentz-Minkowski 3-space asserts that if a maximal surface has a…
Null hypersurfaces in Lorentzian manifolds with the null energy condition
Shintaro Akamine, Atsufumi Honda, Masaaki Umehara +1
Let be a light-like geodesically complete Lorentzian -manifold satisfying the null energy condition. We show that null hypersurfaces properly immersed in $M^{n+1…
Duality of boundary value problems for minimal and maximal surfaces
Shintaro Akamine, Hiroki Fujino
In 1966, Jenkins and Serrin gave existence and uniqueness results for infinite boundary value problems of minimal surfaces in the Euclidean space, and after that such solutions hav…
Bernstein-type theorem for zero mean curvature hypersurfaces without time-like points in Lorentz-Minkowski space
Shintaro Akamine, Atsufumi Honda, Masaaki Umehara +1
Calabi and Cheng-Yau's Bernstein-type theorem asserts that an entire zero mean curvature graph in Lorentz-Minkowski -space which admits only space-li…
Space-like maximal surfaces containing entire null lines in Lorentz-Minkowski 3-space
Shintaro Akamine, Masaaki Umehara, Kotaro Yamada
Consider a surface immersed in the Lorentz-Minkowski 3-space . A complete light-like line in is called an entire null line on the surface…
Improvement of the Bernstein-type theorem for space-like zero mean curvature graphs in Lorentz-Minkowski space using fluid mechanical duality
Shintaro Akamine, Masaaki Umehara, Kotaro Yamada
Calabi's Bernstein-type theorem asserts that a zero mean curvature entire graph in Lorentz-Minkowski space which admits only space-like points is a space-like pla…