On regular algebraic surfaces of R³ with constant mean curvature

2014/03/27 by J. Lucas M. Barbosa, João Lucas Marques Barbosa, Barbosa, João Lucas Marques +2
Mathematics · #Algebraic Geometry and Number Theory #Geometric Analysis and Curvature Flows #Holomorphic and Operator Theory #math.DG #msc:53C42

paper · pdf · doi:10.48550/arxiv.1403.7029

arxiv created 2014/03/27 · arxiv updated 2014/03/28

Abstract

We consider regular surfaces M that are given as the zeros of a polynomial function p:R³→ 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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