Price Inequalities and Betti Number Growth on Manifolds without Conjugate Points

2017/04/20 by Luca F. Di Cerbo, Di Cerbo, Luca F., Mark J. Stern +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1704.06354

openalex publication_date 2017/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We derive Price inequalities for harmonic forms on manifolds without conjugate points and with a negative Ricci upper bound. The techniques employed in the proof work particularly well for manifolds of non-positive sectional curvature, and in this case we prove a strengthened Price inequality. We employ these inequalities to study the asymptotic behavior of the Betti numbers of coverings of Riemannian manifolds without conjugate points. Finally, we give a vanishing result for L²-Betti numbers of closed manifolds without conjugate points.

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