Globally subanalytic CMC surfaces in $\mathbb{R}^3$
  We prove that globally subanalytic nonsingular CMC surfaces of $\mathbb{R}^3$ are only planes, round spheres or right circular cylinders 
Jo\~ao Lucas M. Barbosa, Lev Birbrair, Manfredo P. do Carmo and   Alexandre Fernandes
math.DG