Height estimates for surfaces with positive constant mean curvature in $\mathbb{M}^{2}\times\mathbb{R}$
Aledo, Juan A. ; Espinar, José M. ; Gálvez, José A.
Illinois J. Math., Tome 52 (2008) no. 1, p. 203-211 / Harvested from Project Euclid
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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 ℝ3, $\mathbb{S}^{2}\times\mathbb{R}$ , and ℍ2×ℝ and we characterize the surfaces for which these bounds are achieved. We also give some geometric properties on properly embedded surfaces without boundary.
Publié le : 2008-05-15
Classification:  53A10,  53C42 
@article{1242414128,
     author = {Aledo, Juan A. and Espinar, Jos\'e M. and G\'alvez, Jos\'e A.},
     title = {Height estimates for surfaces with positive constant mean curvature in $\mathbb{M}^{2}\times\mathbb{R}$},
     journal = {Illinois J. Math.},
     volume = {52},
     number = {1},
     year = {2008},
     pages = { 203-211},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1242414128}
}

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., Tome 52 (2008) no. 1, pp.  203-211. http://gdmltest.u-ga.fr/item/1242414128/