Nonexistence of positively expansive maps on compact connected manifolds with boundary

Abstract

Abstract.In this note we prove that no compact connected manifold with boundary admits a positively expansive map.

Positively expansive homeomorphisms on compact metric spaces

“…Remark 2. In Claim 1 we can assume that d h i (u n ), h i (v n ) c for 0 < i < k n since, if not, we can replace u n and v n by some h i (u n ) and h i (v n ). In addition, by (2) in Claim 1, we have k n > n.…”

Nonexistence of codimension one Anosov flows on compact manifolds with boundary

“…A related work is [10], where it is proved the non-existence of positively expanding maps on compact manifolds with boundary. See also [6,Section 5,p.…”