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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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.

Article information

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

Dates
First available in Project Euclid: 15 May 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1242414128

Digital Object Identifier
doi:10.1215/ijm/1242414128

Mathematical Reviews number (MathSciNet)
MR2507241

Zentralblatt MATH identifier
1166.53039

Subjects
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]

Citation

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. https://projecteuclid.org/euclid.ijm/1242414128


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References

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