| Autor: |
Barreto, Alexandre Paiva, Fontenele, Francisco, Hartmann, Luiz |
| Předmět: |
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| Zdroj: |
Proceedings of the Royal Society of Edinburgh: Section A: Mathematics; Aug2022, Vol. 152 Issue 4, p1081-1088, 8p |
| Abstrakt: |
We prove that there are no regular algebraic hypersurfaces with non-zero constant mean curvature in the Euclidean space $\mathbb {R}^{n+1},\,\;n\geq 2,$ defined by polynomials of odd degree. Also we prove that the hyperspheres and the round cylinders are the only regular algebraic hypersurfaces with non-zero constant mean curvature in $\mathbb {R}^{n+1}, n\geq 2,$ defined by polynomials of degree less than or equal to three. These results give partial answers to a question raised by Barbosa and do Carmo. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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