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A second derivative formula of the Liouville entropy atspaces of constant negative curvature
Published online by Cambridge University Press: 12 April 2001
Abstract
In this paper we study a new functional on the space of metrics with negative curvature on a compact manifold. It is a linear combination of Liouville entropy and total scalar curvature. Locally symmetric spaces are critical points of this functional. We provide an explicit formula for its second derivative at metrics of constant negative curvature. In particular, this shows that a metric of constant curvature is a local maximum.
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- 1997 Cambridge University Press
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