Princípio do máximo relacionado ao crescimento de volume

Abstract

In this Dissertation, it is presented a new form of maximum principle for smooth functions on a complete noncompact Riemannian manifold M for which there exists a bounded vector field X such that its inner product with the gradient of a function f is greather than or equal to zero on M and its divergent is greather than or equal af outside a suitable compact subset of M, for some positive constant a, under the assumption that M has either polynomial or exponential volume growth. We then use it to obtain some Bernstein-type results for hypersurfaces immersed into a Riemannian manifold endowed with a Killing vector field, as well as to obtain some results on the existence and the size of minimal submanifolds immersed into a Riemannian manifold endowed with a closed conformal vector field.