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arXiv · 1403.7029

On regular algebraic surfaces of $R^3$ with constant mean curvature

João Lucas Marques Barbosa·Manfredo Perdigão do Carmo
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Abstract

We consider regular surfaces $M$ that are given as the zeros of a polynomial function $p:R^3\rightarrow R$, where the gradient of $p$ vanishes nowhere. We assume that $M$ has non-zero mean curvature and prove that there exist only two examples of such surfaces, namely the sphere and the circular cylinder.

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João Lucas Marques Barbosa, Manfredo Perdigão do Carmo. 2014-03-27. On regular algebraic surfaces of $R^3$ with constant mean curvature. https://arxiv.org/abs/1403.7029

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