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Price Inequalities and Betti Number Growth on Manifolds without Conjugate Points. (arXiv:1704.06354v1 [math.DG])
来源于:arXiv
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. 查看全文>>