Eigenvalue estimates for the drifting Laplacian and the p-Laplacian on submanifolds of warped products. Issue 11 (18th August 2021)

• Record Type: Journal Article
• Authors: Lu, Wei; Mao, Jing; Wu, Chuan-Xi; Zeng, Ling-Zhong
• Is Part Of: Applicable analysis. Volume 100:Issue 11(2021)
• Page Start: 2275
• Page End: 2300
• Publication Date: 2021-08-18
• Subjects: Salvatore Leonardi; Eigenvalues -- spherically symmetric manifolds -- the drifting Laplacian -- p-Laplacian -- warped products; 53C40 -- 53C42 -- 58C40; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2019.1679793
• Languages: English
• ISSNs: 0003-6811

Abstract

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.