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

Fuente: arXiv
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Main Authors: Akamine, Shintaro, Lee, Wonjoo, Yang, Seong-Deog
Format: Preprint
Published: 2025
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author Akamine, Shintaro
Lee, Wonjoo
Yang, Seong-Deog
author_facet Akamine, Shintaro
Lee, Wonjoo
Yang, Seong-Deog
contents 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 $\mathbb{I}^3$.
format Preprint
id arxiv_https___arxiv_org_abs_2505_24109
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Bernstein-type theorem for constant mean curvature surfaces in the isotropic 3-space
Akamine, Shintaro
Lee, Wonjoo
Yang, Seong-Deog
Differential Geometry
Primary 53A10, Secondary 53B30, 35B08
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 $\mathbb{I}^3$.
title Bernstein-type theorem for constant mean curvature surfaces in the isotropic 3-space
topic Differential Geometry
Primary 53A10, Secondary 53B30, 35B08
url https://arxiv.org/abs/2505.24109