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Abstract On a complete Riemannian manifold (M, g), we consider L^p₋₎₂ Llocp distributional solutions of the differential inequality - u + u 0 -Δu+λu≥0 with >0 λ>0 a locally bounded function that may decay to 0 at infinity. Under suitable growth conditions on the L^p Lp norm of u over geodesic balls, we obtain that any such solution must be nonnegative. This is a kind of generalized L^p Lp -preservation property that can be read as a Liouville-type property for nonnegative subsolutiuons of the equation u u Δu≥λu. An application of the analytic results to L^p Lp growth estimates of the extrinsic distance of complete minimal submanifolds is also given.
Bisterzo et al. (Sat,) studied this question.
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