Differential Inequalities on Complete Riemannian Manifolds and Applications

This paper treats various aspects of the asymptotic behavior of solutions of certain elliptic equations of geometric interest on complete Riemannian manifolds. Sharp results relating the rate of volume growth of a complete Riemannian manifold and the growth of its harmonic and subharmonic functions can be found in E22] together with references to related results. In Sect. 2 of this paper we consider solutions of the more restrictive inequality Au>=e>O (where = div o grad) and show that these must be unbounded if M n has even quadratically exponential volume growth, and that u must have faster than linear growth if