Abstract
Understanding and finding of general algebraic constant mean curvature surfaces in the Euclidean spaces is a hard open problem. The basic examples are the standard spheres and the round cylinders, all defined by a polynomial of degree 2. In this paper, we prove that there are no algebraic hypersurfaces of degree 3 in \(\mathbb {R}^n\), \(n\ge 3\), with nonzero constant mean curvature.
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Acknowledgements
This work was done while the first author visited Linköping University. He would like to thank the Mathematical Institution of Linköping University for hospitality. The second author acknowledges support from G D Magnusons Fond, MG2017-0101.
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Perdomo, O., Tkachev, V.G. Algebraic CMC hypersurfaces of order 3 in Euclidean spaces. J. Geom. 110, 6 (2019). https://doi.org/10.1007/s00022-018-0461-z
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DOI: https://doi.org/10.1007/s00022-018-0461-z