Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-07T22:31:34.653Z Has data issue: false hasContentIssue false
  • English
  • Français

On minimal maps of 2-manifolds

Published online by Cambridge University Press:  22 December 2004

ALEXANDER BLOKH ,
LEX OVERSTEEGEN  and
E. D. TYMCHATYN
ALEXANDER BLOKH
Affiliation:
Department of Mathematics, University of Alabama at Birmingham, Birmingham, AL 35294-1170, USA (e-mail: [email protected], [email protected])
LEX OVERSTEEGEN
Affiliation:
Department of Mathematics, University of Alabama at Birmingham, Birmingham, AL 35294-1170, USA (e-mail: [email protected], [email protected])
E. D. TYMCHATYN
Affiliation:
Mathematical Department, University of Saskatchewan, Canada (e-mail: [email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

We prove that a minimal self-mapping of a compact 2-manifold has tree-like fibers (i.e. all points have preimages which are connected, at most one-dimensional and with trivial shape). We also prove that the only 2-manifolds (compact or not) which admit minimal maps are either finite unions of tori, or finite unions of Klein bottles.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 25 , Issue 1 , February 2005 , pp. 41 - 57
Copyright
2004 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)