Abstract
We study the asymmetry of the Lipschitz metric d on Outer space. We introduce
an (asymmetric) Finsler norm that induces d. There is an Out(F_n)-invariant
potential \Psi on Outer space such that when the Lipschitz norm is corrected by
the derivative of \Psi, the resulting norm is quasisymmetric. As an
application, we give new proofs of two theorems of Handel-Mosher, that the
Lipschitz metric is quasi-symmetric when restricted to a thick part of Outer
space, and that there is a uniform bound, depending only on the rank, on the
ratio of logs of growth rates of any irreducible outer automorphism f in
Out(F_n) and its inverse.
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