O Princípio de Omori-Yau para os operadores Lr e aplicações

Abstract

The objective of this work is to establish a theorem of the type Omori-Yau for operators Lr, (see Theorem 3.1), since such operators are a natural generalization of the Laplacian and under the conditions of this theorem, to deduce some applications such as: The Jorge-Xavier type theorem [J-X]) for curvatures of order greater than one, (Theorem 4.1); Non-existence of hypersurfaces of JRn + 1 with Hr + 1 identically zero (Theorem 4.2); We study the inequality Lru 2: dash (~ ·) f (u) which is a more general version of inequality, 6.u 2: f (u), studied by Vau [Y] according to Theorem (4.3); Finally, we obtained a result similar to that obtained by Vau mentioned in item (2).