A sharp upper bound for the first eigenvalue of the Laplacian of compact hypersurfaces in rank-1 symmetric spaces

2007/09/21 by G. Santhanam, Santhanam, G.
Mathematics · #53C20 #53C40 #53C42 #Analytic and geometric function theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Metric Geometry (math.MG) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.0709.3349

openalex publication_date 2007/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let M be a closed hypersurface in a simply connected rank-1 symmetric space \olm. In this paper, we give an upper bound for the first eigenvalue of the Laplacian of M in terms of the Ricci curvature of \olm and the square of the length of the second fundamental form of the geodesic spheres with center at the center-of-mass of M.

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