On minimal maps of 2-manifolds

Academic Article

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.
  • Published In

    Digital Object Identifier (doi)

    Author List

  • Blokh A; Oversteegen L; Tymchatyn ED
  • Start Page

  • 41
  • End Page

  • 57
  • Volume

  • 25
  • Issue

  • 1