Eigenvalue estimates for submanifolds in Hadamard manifolds and product manifolds N×ℝ

2018/05/24 by Jing Mao, Mao, Jing, Rong-Qiang Tu +3
Mathematics · #53C40 #53C42 #58C40 #Bounded function #Computer science #Curvature #Differential Geometry (math.DG) #Eigenvalues and eigenvectors #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry #Hadamard product #Hadamard three-lines theorem #Hadamard transform #Hyperbolic space #Laplace operator #Mathematical analysis #Mathematics #Mean curvature #Nonlinear Partial Differential Equations #Physics #Product (mathematics) #Pure mathematics #Space (punctuation) #math.DG #msc:53C40 #msc:53C42 #msc:58C40

paper · pdf · doi:10.48550/arxiv.1805.09565

published in arXiv (Cornell University) (Cornell University) · The first version of this paper was finished in December 2017. Comments are welcome. 22 pages. A slightly revised version will appear in Hiroshima Mathematical Journal

openalex publication_date 2018/05/24 · arxiv created 2019/09/04 · arxiv updated 2019/09/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

In this paper, we investigate submanifolds with locally bounded mean curvature in Hadamard manifolds, product manifolds N×ℝ, submanifolds with bounded φ-mean curvature in the hyperbolic space, and successfully give lower bounds for the weighted fundamental tone and the first eigenvalue of the p-Laplacian.

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