Abstract
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.
Citation
Juan A. Aledo. José M. Espinar. José A. Gálvez. "Height estimates for surfaces with positive constant mean curvature in $\mathbb{M}^{2}\times\mathbb{R}$." Illinois J. Math. 52 (1) 203 - 211, Spring 2008. https://doi.org/10.1215/ijm/1242414128
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