Height estimates for surfaces with positive constant mean curvature in \(\mathbb M^2\times\mathbb R\). (English) Zbl 1166.53039
Summary: 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 \(\mathbb R^3\), \(\mathbb S^2\times\mathbb R\), and \(\mathbb H^2\times \mathbb R\) and we characterize the surfaces for which these bounds are achieved. We also give some geometric properties on properly embedded surfaces without boundary.
MSC:
| 53C42 | Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) |
| 53A10 | Minimal surfaces in differential geometry, surfaces with prescribed mean curvature |
References:
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