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Globally subanalytic CMC surfaces in \(\mathbb{R}^3\). (English) Zbl 1407.32002

Summary: We prove that globally subanalytic nonsingular CMC surfaces of \(\mathbb R^3\) are only planes, round spheres, or right circular cylinders.

MSC:

32B20 Semi-analytic sets, subanalytic sets, and generalizations
53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions
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