arXiv subjects
Publications and source records attributed to Marcos Petrúcio Cavalcante.
We prove that there are no minimal hypersurfaces properly immersed in any region of the Euclidean space bounded by unstable minimal cones. We also prove the analogous result for $r$-minimal hypersurfaces.
In this paper we obtain lower bound estimates of the spectrum of Laplace-Beltrami operator on complete submanifolds with bounded mean curvature, whose ambient space admits a Riemannian submersion over a Riemannian manifold with negative sectional curvature. Our main theorem generalizes many previous known estimates and applies for both immersions and submersions.