Metric stability of trees and tight spans
- Lang, Urs Department of Mathematics, ETH Zurich, Switzerland
- Pavón, Maël Department of Mathematics, ETH Zurich, Switzerland
- Züst, Roger Département de Mathématiques, Université de Fribourg, Switzerland
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01.07.2013
Published in:
- Archiv der Mathematik. - 2013, vol. 101, no. 1, p. 91–100
English
We prove optimal extension results for roughly isometric relations between metric ( R R -)trees and injective metric spaces. This yields sharp stability estimates, in terms of the Gromov–Hausdorff (GH) distance, for certain metric spanning constructions: the GH distance of two metric trees spanned by some subsets is smaller than or equal to the GH distance of these sets. The GH distance of the injective hulls, or tight spans, of two metric spaces is at most twice the GH distance between themselves.
- Faculty
- Faculté des sciences et de médecine
- Department
- Département de Mathématiques
- Language
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- English
- Classification
- Mathematics
- License
- License undefined
- Identifiers
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- RERO DOC 118037
- DOI 10.1007/s00013-013-0535-y
- Persistent URL
- https://folia.unifr.ch/unifr/documents/302994
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