Some Results on Maps That Factor through a Tree

Roger Züst

Analysis and Geometry in Metric Spaces (2015)

  • Volume: 3, Issue: 1, page 73-92, electronic only
  • ISSN: 2299-3274

Abstract

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We give a necessary and sufficient condition for a map deffned on a simply-connected quasi-convex metric space to factor through a tree. In case the target is the Euclidean plane and the map is Hölder continuous with exponent bigger than 1/2, such maps can be characterized by the vanishing of some integrals over winding number functions. This in particular shows that if the target is the Heisenberg group equipped with the Carnot-Carathéodory metric and the Hölder exponent of the map is bigger than 2/3, the map factors through a tree.

How to cite

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Roger Züst. "Some Results on Maps That Factor through a Tree." Analysis and Geometry in Metric Spaces 3.1 (2015): 73-92, electronic only. <http://eudml.org/doc/269944>.

@article{RogerZüst2015,
abstract = {We give a necessary and sufficient condition for a map deffned on a simply-connected quasi-convex metric space to factor through a tree. In case the target is the Euclidean plane and the map is Hölder continuous with exponent bigger than 1/2, such maps can be characterized by the vanishing of some integrals over winding number functions. This in particular shows that if the target is the Heisenberg group equipped with the Carnot-Carathéodory metric and the Hölder exponent of the map is bigger than 2/3, the map factors through a tree.},
author = {Roger Züst},
journal = {Analysis and Geometry in Metric Spaces},
keywords = {trees; Heisenberg group; Stieltjes-Integral; currents; winding number; tree; Stieltjes-integral; Hölder continuous; Lipschitz},
language = {eng},
number = {1},
pages = {73-92, electronic only},
title = {Some Results on Maps That Factor through a Tree},
url = {http://eudml.org/doc/269944},
volume = {3},
year = {2015},
}

TY - JOUR
AU - Roger Züst
TI - Some Results on Maps That Factor through a Tree
JO - Analysis and Geometry in Metric Spaces
PY - 2015
VL - 3
IS - 1
SP - 73
EP - 92, electronic only
AB - We give a necessary and sufficient condition for a map deffned on a simply-connected quasi-convex metric space to factor through a tree. In case the target is the Euclidean plane and the map is Hölder continuous with exponent bigger than 1/2, such maps can be characterized by the vanishing of some integrals over winding number functions. This in particular shows that if the target is the Heisenberg group equipped with the Carnot-Carathéodory metric and the Hölder exponent of the map is bigger than 2/3, the map factors through a tree.
LA - eng
KW - trees; Heisenberg group; Stieltjes-Integral; currents; winding number; tree; Stieltjes-integral; Hölder continuous; Lipschitz
UR - http://eudml.org/doc/269944
ER -

References

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