The Volume Entropy of a Riemannian Metric Evolving by the Ricci Flow on a Manifold of Dimension 3 or Above

Details The Volume Entropy of a Riemannian Metric Evolving by the Ricci Flow on a Manifold of Dimension 3 or Above The Volume Entropy of a Riemannian Metric Evolving by the Ricci Flow on a Manifold of Dimension 3 or Above

2006-04-16

arxiv.org/abs/math/0604355v2

Mathematics

Differential Geometry

5 pages

Scientific paper

In this paper it is proven that the volume entropy of a riemannian metric
evolving by the Ricci flow, if does not collapse, nondecreases. Therefore, it
provides a sufficient condition for a solution to collapse. Then, for the limit
solutions of type I or III, the limit entropy is the limit of the entropy as
$t$ approaches the singular (finite or not) time.

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