ALGEBRAIC CONSTANT MEAN CURVATURE SURFACES IN EUCLIDEAN SPACE

作者：Perdomo Oscar M^*

来源：Houston Journal of Mathematics, 2013, 39(1): 127-136.

• Constant mean curvature
• Algebraic surfaces
• Grobner Bases

In this paper we prove that the only algebraic constant mean curvature (cmc) surfaces in R-3 of order less than four are the planes, the spheres and the cylinders. The method used heavily depends on the efficiency of algorithms to compute Grobner Bases and also on the memory capacity of the computer used to do the computations. We will also prove that the problem of finding algebraic constant mean curvature hypersurfaces in the Euclidean space completely reduces to the problem of solving a system of polynomial equations.

• 出版日期2013