$\mathbb H^2\times\mathbb R中常平均曲率曲面的Slab定理和半空间定理$

IF 1.3 2区数学 Q1 MATHEMATICS

Revista Matematica Iberoamericana Pub Date : 2021-05-24 DOI:10.4171/rmi/1372

L. Hauswirth, Ana Menezes, Magdalena Rodríguez

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摘要

我们证明了在H2×R中，具有常平均曲率0本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Slab theorem and halfspace theorem for constant mean curvature surfaces in $\mathbb H^2\times\mathbb R$

We prove that a properly embedded annular end of a surface in H 2 × R with constant mean curvature 0 < H ≤ 12 can not be contained in any horizontal slab. Moreover, we show that a properly embedded surface with constant mean curvature 0 < H ≤ 12 contained in H 2 × [0 , + ∞ ) and with ﬁnite topology is necessarily a graph over a simply connected domain of H 2 . For the case H = 12 , the graph is entire. 2020 Mathematics Subject Classiﬁcation: 53C30, 53A10.