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The minimal entropy problem for 3-manifolds with zero simplicial volume

James W. Anderson·Gabriel P. Paternain
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Abstract

We consider the minimal entropy problem, namely the question of whether there exists a smooth metric of minimal entropy, for certain classes of 3-manifolds. Among other resulsts, we show that if M is a closed, orientable, geometrizable 3-manifold with zero simplicial volume, then the minimal entropy can be solved for M if and only if M admits a metric modelled on 4 of the 8 standard 3-dimensional geometries, namely $S^3$, $S^2\times R$, $E^3$, or Nil.

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James W. Anderson, Gabriel P. Paternain. 2000-11-21. The minimal entropy problem for 3-manifolds with zero simplicial volume. https://arxiv.org/abs/math/0011153

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