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arXiv · 2505.24109

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

Shintaro Akamine·Wonjoo Lee·Seong-Deog Yang
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Abstract

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

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Shintaro Akamine, Wonjoo Lee, Seong-Deog Yang. 2025-05-30. Bernstein-type theorem for constant mean curvature surfaces in the isotropic 3-space. https://arxiv.org/abs/2505.24109

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