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Publications [#340296] of Mark A. Stern

Papers Published

  1. Cerbo, LFD; Stern, M, Price Inequalities and Betti Number Growth on Manifolds without Conjugate Points, Communications in Analysis and Geometry (August, 2019), International Press
    (last updated on 2021/05/09)

    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 $L^{2}$-Betti numbers of closed manifolds without conjugate points.
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