The spectrum of the Laplacian and volume growth of proper minimal submanifolds

2021/04/05 by G. Pacelli Bessa, Vicent Gimeno, Bessa, G. Pacelli +3
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2104.01979

openalex publication_date 2021/04/05 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

We give upper bounds for the bottom of the essential spectrum of properly immersed minimal submanifolds of ℝⁿ in terms of their volume growth. Our result improves the extrinsic version of Brook's essential spectrum estimate given by Ilias-Nelli-Soret in \cite[Cor.3]ins.

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