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Maximal ergodic theorems and applications to Riemannian geometry

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Abstract

We prove new ergodic theorems in the context of infinite ergodic theory, and give some applications to Riemannian and Kähler manifolds without conjugate points. One of the consequences of these ideas is that a complete manifold without conjugate points has nonpositive integral of the infimum of Ricci curvatures, whenever this integral makes sense. We also show that a complete Kähler manifold with nonnegative holomorphic curvature is flat if it has no conjugate points.

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Authors and Affiliations

  1. Instituto de Matemática, Universidade Federal Fluminense (UFF), Rua Mário Santos Braga S/N. Valonguinho, 24.020-140, Niterói, RJ, Brazil

    Sérgio Mendonça & Detang Zhou

Authors
  1. Sérgio Mendonça
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  2. Detang Zhou
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Corresponding author

Correspondence to Sérgio Mendonça.

Additional information

The first author dedicates this paper to his parents José Martiniano and Zoraide

Both authors are partially supported by CNPq, Brazil.

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Mendonça, S., Zhou, D. Maximal ergodic theorems and applications to Riemannian geometry. Isr. J. Math. 139, 319–335 (2004). https://doi.org/10.1007/BF02787554

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  • DOI: https://doi.org/10.1007/BF02787554

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