# Some Results on Maps That Factor through a Tree

Analysis and Geometry in Metric Spaces (2015)

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

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topRoger 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 -

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