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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access March 19, 2015

Some Results on Maps That Factor through a Tree

  • Roger Züst


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.


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Received: 2014-9-30
Accepted: 2015-3-12
Published Online: 2015-3-19

© 2015 Roger Züst

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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