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The volume entropy of a surface decreases along the Ricci flow

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Manning, Anthony. (2004) The volume entropy of a surface decreases along the Ricci flow. Ergodic Theory and Dynamical Systems, Vol.24 (No.1). pp. 171-176. ISSN 0143-3857

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Official URL: http://dx.doi.org/10.1017/S0143385703000415

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.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH):	Riemannian manifolds, Ricci flow, Ergodic theory, Surfaces, Algebraic, Entropy (Information theory)
Journal or Publication Title:	Ergodic Theory and Dynamical Systems
Publisher:	Cambridge University Press
ISSN:	0143-3857
Date:	February 2004
Volume:	Vol.24
Number:	No.1
Page Range:	pp. 171-176
Identification Number:	10.1017/S0143385703000415
Status:	Peer Reviewed
Access rights to Published version:	Open Access
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URI:	http://wrap.warwick.ac.uk/id/eprint/747