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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. 171176. ISSN 01433857

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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:  01433857 
Date:  February 2004 
Volume:  Vol.24 
Number:  No.1 
Page Range:  pp. 171176 
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 
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