Some Results on Maps That Factor through a Tree

• Autorzy: Roger Züst
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

Kategorie tematyczne

• 55M25: Degree, winding number
• 26A42: Integrals of Riemann, Stieltjes and Lebesgue type
• 49Q15: Geometric measure and integration theory, integral and normal currents

• Wydawca: De Gruyter Open
• Czasopismo: Analysis and Geometry in Metric Spaces
• Rocznik: 2015
• Tom: 3
• Numer: 1

Daty

otrzymano

2014-09-30

zaakceptowano

2015-03-12

online

2015-03-19

Twórcy

autor

Roger Züst

• Institut de Mathématiques de Jussieu, Bâtiment Sophie Germain, 75205 Paris, France

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Identyfikatory

DOI

10.1515/agms-2015-0005