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The volume entropy of a surface decreases along the Ricci flow

Published online by Cambridge University Press:  02 February 2004

ANTHONY MANNING
ANTHONY MANNING
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK (e-mail: akm@maths.warwick.ac.uk)
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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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 24 , Issue 1 , February 2004 , pp. 171 - 176
Copyright
2004 Cambridge University Press

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