LAUSR

ABSTRACT In this paper, we investigate minimal submanifolds M immersed into warped products of type , where is positive, and can give lower bounds for the weighted fundamental tone of the drifting Laplacian, the first eigenvalue of the p-Laplacian on open domains in M. This achievement enables us to deal with spectral estimates for minimal submanifolds bounded by cylinders, cones, spheres and pseudo-hyperbolic spaces, and meanwhile some interesting byproducts can be obtained. For instance, we can show that the fundamental tone of any cylindrically bounded minimal hypersurface in the Euclidean m-space ( ) is positive.