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- W2073456028 abstract "We study the classification of immersed constant mean curvature (CMC) spheres in the homogeneous Riemannian 3-manifold Sol_3, i.e., the only Thurston 3-dimensional geometry where this problem remains open. Our main result states that, for every H>1/(sqrt{3}), there exists a unique (up to left translations) immersed CMC H sphere S_H in Sol_3 (Hopf-type theorem). Moreover, this sphere S_H is embedded, and is therefore the unique (up to left translations) compact embedded CMC H surface in Sol_3 (Alexandrov-type theorem). The uniqueness parts of these results are also obtained for all real numbers H such that there exists a solution of the isoperimetric problem with mean curvature H." @default.
- W2073456028 created "2016-06-24" @default.
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- W2073456028 date "2013-01-01" @default.
- W2073456028 modified "2023-10-03" @default.
- W2073456028 title "Existence and uniqueness of constant mean curvature spheres in Sol 3" @default.
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