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Analysis and Geometry in Metric Spaces

Ed. by Ritoré, Manuel

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Some Results on Maps That Factor through a Tree

Roger Züst
  • Corresponding author
  • Institut de Mathématiques de Jussieu, Bâtiment Sophie Germain, 75205 Paris, France
  • Other articles by this author:
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Published Online: 2015-03-19 | DOI: https://doi.org/10.1515/agms-2015-0005


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.

Keywords: trees; Heisenberg group; Stieltjes-Integral; currents; winding number

MSC: Primary: 51F, 30L; Secondary: 49Q15, 26A42, 55M25


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About the article

Received: 2014-09-30

Accepted: 2015-03-12

Published Online: 2015-03-19

Citation Information: Analysis and Geometry in Metric Spaces, Volume 3, Issue 1, ISSN (Online) 2299-3274, DOI: https://doi.org/10.1515/agms-2015-0005.

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© 2015 Roger Züst. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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