Construction of compact constant mean curvature hypersurfaces with topology (Q442127)
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scientific article; zbMATH DE number 6064518
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Construction of compact constant mean curvature hypersurfaces with topology |
scientific article; zbMATH DE number 6064518 |
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Construction of compact constant mean curvature hypersurfaces with topology (English)
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9 August 2012
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In the paper under review the author uses the end-to-end gluing of constant mean curvature surface developed by \textit{J. Ratzkin} in his PhD thesis [``An end-to-end construction of constant mean curvature'', Univ. Washington (2001)] and the moduli space theory investigated by \textit{R. Kusner}, \textit{R. Mazzeo} and \textit{D. Pollack} [Geom. Funct. Anal. 6, No. 1, 120--137 (1996; Zbl 0966.58005)] to produce compact constant mean curvature hypersurfaces with nontrivial topology. To simplify reasonings the author assumes that considered hypersurfaces have a large group of symmetry but his method can be obviously used to give surfaces with less symmetries.
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mean curvature
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compact hypersurface
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end-to-end construction
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moduli space theory
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Jacobi operator
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