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Surfaces of finite type with constant mean curvature. (English) Zbl 0828.53006

The authors prove the following results for finite type surfaces in the Euclidean 3-space \(E^3\). Theorem 1: A 3-type surface in \(E^3\) has nonconstant mean curvature. Theorem 2: Ordinary spheres, planes, catenoids and circular cylinders are the only surfaces of revolution with constant mean curvature in \(E^3\) which are of finite type.

MSC:

53A05 Surfaces in Euclidean and related spaces
53B25 Local submanifolds
58J50 Spectral problems; spectral geometry; scattering theory on manifolds
53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
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