We prove a version of the strong half-space theorem between the classes of recurrent minimal surfaces and complete minimal surfaces with bounded curvature of R 3 . We also show that any minimal hypersurface immersed with bounded curvature in MˆR`equals some Mˆtsu provided M is a complete, recurrent n-dimensional Riemannian manifold with Ric M ě 0 and whose sectional curvatures are bounded from above. For H-surfaces we prove that a stochastically complete surface M can not be in the mean convex side of a H-surface N embedded in R 3 with bounded curvature if sup |H M | ă H, or distpM, N q " 0 when sup |H M | " H. Finally, a maximum principle at infinity is shown assuming M has non-empty boundary.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.