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SOME REMARKS ON THE PIGOLA–RIGOLI–SETTI VERSION OF THE OMORI–YAU MAXIMUM PRINCIPLE
Published online by Cambridge University Press: 19 August 2013
Abstract
We prove that the hypotheses in the Pigola–Rigoli–Setti version of the Omori–Yau maximum principle are logically equivalent to the assumption that the manifold carries a ${C}^{2} $ proper function whose gradient and Hessian (Laplacian) are bounded. In particular, this result extends the scope of the original Omori–Yau principle, formulated in terms of lower bounds for curvature.
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- Copyright ©2013 Australian Mathematical Publishing Association Inc.
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