On regular algebraic hypersurfaces with non-zero constant mean curvature in Euclidean spaces

Alexandre Paiva Barreto, Francisco Fontenele, Luiz Hartmann

We prove that there are no regular algebraic hypersurfaces with non-zero constant mean curvature in the Euclidean space ${\mathbb{R}}^{n+1}$, $n\ge 2$, defined by polynomials of odd…