Gluing Hyperconvex Metric Spaces
Analysis and Geometry in Metric Spaces (2015)
- Volume: 3, Issue: 1, page 102-110, electronic only
- ISSN: 2299-3274
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topBenjamin Miesch. "Gluing Hyperconvex Metric Spaces." Analysis and Geometry in Metric Spaces 3.1 (2015): 102-110, electronic only. <http://eudml.org/doc/271074>.
@article{BenjaminMiesch2015,
abstract = {We investigate how to glue hyperconvex (or injective) metric spaces such that the resulting space remains hyperconvex. We give two new criteria, saying that on the one hand gluing along strongly convex subsets and on the other hand gluing along externally hyperconvex subsets leads to hyperconvex spaces. Furthermore, we show by an example that these two cases where gluing works are opposed and cannot be combined.},
author = {Benjamin Miesch},
journal = {Analysis and Geometry in Metric Spaces},
keywords = {hyperconvex spaces; injective metric spaces; strongly convex; externally hyperconvex},
language = {eng},
number = {1},
pages = {102-110, electronic only},
title = {Gluing Hyperconvex Metric Spaces},
url = {http://eudml.org/doc/271074},
volume = {3},
year = {2015},
}
TY - JOUR
AU - Benjamin Miesch
TI - Gluing Hyperconvex Metric Spaces
JO - Analysis and Geometry in Metric Spaces
PY - 2015
VL - 3
IS - 1
SP - 102
EP - 110, electronic only
AB - We investigate how to glue hyperconvex (or injective) metric spaces such that the resulting space remains hyperconvex. We give two new criteria, saying that on the one hand gluing along strongly convex subsets and on the other hand gluing along externally hyperconvex subsets leads to hyperconvex spaces. Furthermore, we show by an example that these two cases where gluing works are opposed and cannot be combined.
LA - eng
KW - hyperconvex spaces; injective metric spaces; strongly convex; externally hyperconvex
UR - http://eudml.org/doc/271074
ER -
References
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- [5] Jie HuaMai and Yun Tang, An injective metrization for collapsible polyhedra, Proc. Amer.Math. Soc. 88 (1983), no. 2, 333–337. [Crossref] Zbl0516.54027
- [6] B. Miesch, Injective Metrics on Cube Complexes, ArXiv e-prints (2014).
- [7] Arvin Moezzi, The injective hull of hyperbolic groups, Ph.D. thesis, ETH Zürich, 2010.
- [8] Bozena Piatek, On the gluing of hyperconvexmetrics and diversities, Ann. Univ. Paedagog. Crac. Stud.Math. 13 (2014), 65–76.
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