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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: ablokh@math.uab.edu, overstee@math.uab.edu)
LEX OVERSTEEGEN
Affiliation:
Department of Mathematics, University of Alabama at Birmingham, Birmingham, AL 35294-1170, USA (e-mail: ablokh@math.uab.edu, overstee@math.uab.edu)
E. D. TYMCHATYN
Affiliation:
Mathematical Department, University of Saskatchewan, Canada (e-mail: tymchat@math.usask.ca)
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Abstract

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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.

Information

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