| THE MINIMAL ENTROPY PROBLEM FOR 3-MANIFOLDS WITH ZERO SIMPLICIAL VOLUME (2007) | |||||||||||||
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| Dedicated to Jacob Palis on his sixtieth birthday Abstract. In this note, we consider the minimal entropy problem, namely the question of whether there exists a smooth metric of minimal entropy, for certain classes of closed 3-manifolds. Specically, we prove the following two results. Theorem A. Let M be a closed orientable irreducible 3-manifold whose fundamental group contains a ZZ subgroup. The following are equivalent: 1. the simplicial volume kMk of M is zero and the minimal entropy problem for M can be solved; 2. M admits a geometric structure modelled on E 3 or Nil; 3. M admits a smooth metric g with h top (g) = 0. Theorem B. Let M be a closed orientable geometrizable 3-manifold. The following are equivalent: 1. the simplicial volume kMk of M is zero and the minimal entropy problem for | |||||||||||||
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