Illinois Journal of Mathematics

Height estimates for surfaces with positive constant mean curvature in $\mathbb{M}^{2}\times\mathbb{R}$

Juan A. Aledo, José M. Espinar, and José A. Gálvez

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We obtain height estimates for compact embedded surfaces with positive constant mean curvature in a Riemannian product space $\mathbb{M}^{2}\times\mathbb{R}$ and boundary on a slice. We prove that these estimates are optimal for the homogeneous spaces $ℝ^3$, $\mathbb{S}^{2}\times\mathbb{R}$, and $ℍ^{2}×ℝ$ and we characterize the surfaces for which these bounds are achieved. We also give some geometric properties on properly embedded surfaces without boundary.

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Illinois J. Math., Volume 52, Number 1 (2008), 203-211.

First available in Project Euclid: 15 May 2009

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Zentralblatt MATH identifier

Primary: 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42] 53C42: Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42]


Aledo, Juan A.; Espinar, José M.; Gálvez, José A. Height estimates for surfaces with positive constant mean curvature in $\mathbb{M}^{2}\times\mathbb{R}$. Illinois J. Math. 52 (2008), no. 1, 203--211. doi:10.1215/ijm/1242414128.

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