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      An optimal inequality between scalar curvature and spectrum of the Laplacian

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          Abstract

          For a Riemannian closed spin manifold and under some topological assumption (non-zero \(\hat{A}\)-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 \(\hat{A}\)-genus. This work improves an inequality which was first proved by K. Ono in 1988.

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          Author and article information

          Journal
          2002-03-26
          2002-03-27
          Article
          math/0203271
          34bed2f4-c160-46c6-b822-c09df1139a05
          History
          Custom metadata
          58J50, 35P15, 46L10, 58G11
          29 pages
          math.DG

          Geometry & Topology
          Geometry & Topology

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