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The volume entropy of a surface decreases along the Ricci flow \ud

By Anthony Manning

Abstract

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

Topics: QA
Publisher: Cambridge University Press
Year: 2004
OAI identifier: oai:wrap.warwick.ac.uk:747

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