An optimal inequality between scalar curvature and spectrum of the Laplacian

2002/03/26 by Hélène Davaux, Davaux, Hélène · 2 citations
Computer Science · Mathematics · #35P15 #46L10 #58G11 #58J50 #Advanced Mathematical Modeling in Engineering #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities #math.DG #msc:35P15 #msc:46L10 #msc:58G11 #msc:58J50

paper · pdf · doi:10.48550/arxiv.math/0203271

29 pages

openalex publication_date 2002/03/26 · arxiv created 2002/03/27 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a Riemannian closed spin manifold and under some topological assumption (non-zero A-genus or enlargeability in the sense of Gromov-Lawson), we give an optimal upper bound for the infimum of the scalar curvature in terms of the first eigenvalue of the Laplacian. The main difficulty lies in the study of the odd-dimensional case. On the other hand, we study the equality case for the closed spin Riemannian manifolds with non-zero A-genus. This work improves an inequality which was first proved by K. Ono in 1988.

Cited by

• The positive mass theorem under a spectral scalar curvature bound on spin manifolds
• Geometric Rigidity via Almost-Harmonic Twisted Spinors

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