In this paper, we study the global geometry of complete, constant mean curvature hypersurfaces embedded in $n$-manifolds. More precisely, we give conditions that imply properness of such surfaces and prove the existence of fixed size one-sided regular neighborhoods for certain constant mean curvature hypersurfaces in certain $n$-manifolds.
William H. Meeks, III. Giuseppe Tinaglia. "Existence of regular neighborhoods for H-surfaces." Illinois J. Math. 55 (3) 835 - 844, Fall 2011. https://doi.org/10.1215/ijm/1369841787