科研之友
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摘要
We study the asymmetry of the Lipschitz metric d on Outer space. We introduce an ( asymmetric) Finsler norm ||.||(L) that induces d. There is an Out (F-n)-invariant "potential" Psi defined on Outer space such that when ||.||(L) is corrected by d Psi, the resulting norm is quasi-symmetric. As an application, we give new proofs of two theorems of Handel-Mosher, that d 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 f is an element of Out (F-n) and its inverse.
- 出版日期2012-2
