Bernstein-type theorem for constant mean curvature surfaces in the isotropic 3-space

2025/05/30 by Akamine, Shintaro, Lee, Wonjoo, Yang, Seong-Deog
#35B08 #Differential Geometry (math.DG) #FOS: Mathematics #Primary 53A10 #Secondary 53B30

paper · doi:10.48550/arxiv.2505.24109

Abstract

There are many non-trivial entire spacelike graphs with constant mean curvature H (CMC H, for short) in the isotropic 3-space \mathbbI³. In this paper, we show a value distribution theorem of Gaussian curvature of complete spacelike constant mean curvature surfaces in \mathbbI³, which implies a Bernstein-type theorem for CMC H graphs in \mathbbI³.

Citations

• A note on isothermic coordinate system for spacelike surfaces with constant mean curvature in Lorentz-Minkowski space
• On the classification of ruled minimal surfaces in pseudo-Euclidean space
• Minimal Varieties in Riemannian Manifolds

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