On the Omori-Yau Maximum Principle and Geometric Applications
  We introduce a version of the Omori-Yau maximum principle which generalizes the version obtained by Pigola-Rigoli-Setti 21. We apply our method to derive a non-trivial generalization Jorge-Koutrofiotis Theorem 15 for cylindrically bounded submanifolds due to Alias-Bessa-Montenegro 2, we extend results due to Alias-Dajczer 5, Alias-Bessa-Dajczer 1 and Alias-Impera-Rigoli 6. 
Barnabe Pessoa LIma and Leandro De Freitas Pessoa
math.DG