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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. doi:10.1017/S0143385703000415 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 | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > 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 | ||||
Official Date: | February 2004 | ||||
Dates: |
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Volume: | Vol.24 | ||||
Number: | No.1 | ||||
Page Range: | pp. 171-176 | ||||
DOI: | 10.1017/S0143385703000415 | ||||
Status: | Peer Reviewed | ||||
Access rights to Published version: | Open Access (Creative Commons) |
Data sourced from Thomson Reuters' Web of Knowledge
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