Half-space theorems for recurrent minimal and -surfaces of
G. Pacelli Bessa
Universidade Federal do Ceará, Fortaleza-Ceará, BrazilLuquesio P. Jorge
Universidade Federal do Ceará, Fortaleza-Ceará, BrazilLeandro F. Pessoa
Universidade Federal do Piauí, Teresina-Piauí, Brazil
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Abstract
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 . 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 equals some provided is a complete, recurrent -dimensional Riemannian manifold with and whose sectional curvatures are bounded from above. Furthermore, we prove a half-space theorem for the class of stochastically complete -surfaces. We present a maximum principle at infinity assuming has non-empty boundary. Finally, we present examples of a complete non-proper recurrent minimal surface with unbounded curvature.
Cite this article
G. Pacelli Bessa, Luquesio P. Jorge, Leandro F. Pessoa, Half-space theorems for recurrent minimal and -surfaces of . Rev. Mat. Iberoam. (2024), published online first
DOI 10.4171/RMI/1498