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  • Cited by 5
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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Jane, Dan and Ruggiero, Rafael O. 2014. Boundary of Anosov dynamics and evolution equations for surfaces. Mathematische Nachrichten, Vol. 287, Issue. 17-18, p. 2002.

    Suárez-Serrato, Pablo and Tapie, Samuel 2012. Conformal entropy rigidity through Yamabe flows. Mathematische Annalen, Vol. 353, Issue. 2, p. 333.

    TAPIE, SAMUEL 2011. A variation formula for the topological entropy of convex-cocompact manifolds. Ergodic Theory and Dynamical Systems, Vol. 31, Issue. 06, p. 1849.

    Thompson, Daniel J. 2011. A criterion for topological entropy to decrease under normalised Ricci flow. Discrete and Continuous Dynamical Systems, Vol. 30, Issue. 4, p. 1243.

    JANE, DAN 2007. An example of how the Ricci flow can increase topological entropy. Ergodic Theory and Dynamical Systems, Vol. 27, Issue. 06,

  • Ergodic Theory and Dynamical Systems, Volume 24, Issue 1
  • February 2004, pp. 171-176

The volume entropy of a surface decreases along the Ricci flow

  • DOI:
  • Published online: 01 February 2004

The volume entropy, h(g), of a compact Riemannian manifold (M,g) measures the growth rate of the volume of a ball of radius R in its universal cover. Under the Ricci flow, g evolves along a certain path $(g_t, t\geq0)$ that improves its curvature properties. For a compact surface of variable negative curvature we use a Katok–Knieper–Weiss formula to show that h(gt) is strictly decreasing.

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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
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