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Volume :39 Issue : 2 2012
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A remark on the Omori-Yau maximum principle
Auther : ALBERT BORBELY
ABSTRACT
A Riemannian manifold is said to satisfy the Omori-Yau maximum principle if for any bounded function there is a sequence , such that , and . It is shown that if the Ricci curvature does not approach too fast the manifold satisfies the Omori-Yau maximum principle. This improves earlier necessary conditions. The given condition is quite optimal.
Keywords: Maximum principle; Sicci convature.