6 papers · 1 filter
Bernstein-type Theorems for constant mean curvature surfaces in the three-dimensional light cone
Shintaro Akamine, Wonjoo Lee, Seong-Deog Yang
We establish Bernstein-type theorems for entire constant mean curvature graphs in the three-dimensional light cone over the horosphere under the assumption that th…
Framed null curves and timelike surfaces via Lorentzian harmonic maps into de-Sitter 2-space
Shintaro Akamine, Hirotaka Kiyohara
We construct a class of Lorentzian harmonic maps into the de-Sitter -space satisfying the eigenvalue equation for the d'Alambert operator and a non-zero co…
Singularities on timelike minimal surfaces in Lorentzian Heisenberg group
Shintaro Akamine, Hirotaka Kiyohara
Timelike minimal surfaces in the three-dimensional Lorentzian Heisenberg group are shown to be constructed from Lorentzian harmonic maps into the de-Sitter two-sphere, and they nat…
Bernstein-type theorem for constant mean curvature surfaces in the isotropic 3-space
Shintaro Akamine, Wonjoo Lee, Seong-Deog Yang
There are many non-trivial entire spacelike graphs with constant mean curvature (CMC , for short) in the isotropic 3-space . In this paper, we show a value dis…
Singularities of generalized timelike minimal surfaces in Lorentz-Minkowski 3-space
Shintaro Akamine
A timelike minimal surface in Minkowski 3-space is a surface whose induced metric is Lorentzian and with vanishing mean curvature. Such surfaces have many kinds of singularities. I…
Null hypersurfaces as wave fronts in Lorentz-Minkowski space
Shintaro Akamine, Atsufumi Honda, Masaaki Umehara +1
In this paper, we show that ``-complete null hypersurfaces'' (i.e. ruled hypersurfaces foliated by entirety of light-like lines) as wave fronts in the -dimensional Lorent…