Constant mean curvature spheres in \(\text{ Sol}_3\) (Q2851616)
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scientific article; zbMATH DE number 6215450
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Constant mean curvature spheres in \(\text{ Sol}_3\) |
scientific article; zbMATH DE number 6215450 |
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14 October 2013
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constant mean curvature spheres
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height estimates
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CMC graphs
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Constant mean curvature spheres in \(\text{ Sol}_3\) (English)
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\(\mathrm{Sol}_3\) is a simply connected homogeneous 3-dimensional manifold whose isometry group has dimension 3 and represents one of the eight models of geometry established by Thurston. For each \(H>0\), the author shows that there exists a unique immersed constant mean curvature (abbreviated, CMC) \(H\) sphere \(S_H\) in \(\mathrm{Sol}_3\). An essential result proved in this paper is the existence of height estimates for certain CMC graphs \(H\) in \(\mathrm{Sol}_3\) that exclusively depend on a fixed positive lower bound for \(H\).
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