Resumen de Half-space theorems for recurrent minimal and H-surfaces of R3

G. Pacelli Bessa, Luquésio Jorge, Leandro F. Pessoa

• 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 R3. The use of subsolutions in the barrier sense allow us to deal with non-proper minimal surfaces immersed with bounded curvature. We show that any minimal hypersurface immersed with bounded curvature in M×R + equals some M×{s} provided M is a complete, recurrent n-dimensional Riemannian manifold with Ric M≥0 and whose sectional curvatures are bounded from above. Furthermore, we prove a half-space theorem for the class of stochastically complete H-surfaces. We present a maximum principle at infinity assuming M has non-empty boundary. Finally, we present examples of a complete non-proper recurrent minimal surface with unbounded curvature.