Eigenvalue estimates for the drifting Laplacian and the p-Laplacian on submanifolds of warped products. Issue 11 (18th August 2021) - Lu, Wei; Mao, Jing; Wu, Chuan-Xi; Zeng, Ling-Zhong
ABSTRACT: In this paper, we investigate minimal submanifolds M immersed into warped products of type N n × f Q q, where f ∈ C ∞ ( N ) 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 R m ( m ≥ 3 ) is positive.