Warianty tytułu
Języki publikacji
Abstrakty
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.
Wydawca
Czasopismo
Rocznik
Tom
Numer
Opis fizyczny
Daty
otrzymano
2015-03-06
zaakceptowano
2015-05-05
online
2015-05-21
Twórcy
autor
- Department of Mathematics, ETH Zürich, 8092 Zürich, Switzerland
Bibliografia
- [1] N. Aronszajn and P. Panitchpakdi, Extension of uniformly continuous transformations and hyperconvex metric spaces, Pacific J. Math. 6 (1956), 405–439.
- [2] Jean-Bernard Baillon, Nonexpansive mapping and hyperconvex spaces, Fixed point theory and its applications (Berkeley, CA, 1986), Contemp. Math., vol. 72, Amer. Math. Soc., Providence, RI, 1988, pp. 11–19.
- [3] Martin R. Bridson and André Haefliger, Metric spaces of non-positive curvature, Grundlehren der Mathematischen Wissenschaften
- [Fundamental Principles of Mathematical Sciences], vol. 319, Springer-Verlag, Berlin, 1999.
- [4] R. Espínola and M. A. Khamsi, Introduction to hyperconvex spaces, Handbook of metric fixed point theory, Kluwer Acad. Publ., Dordrecht, 2001, pp. 391–435.
- [5] Jie HuaMai and Yun Tang, An injective metrization for collapsible polyhedra, Proc. Amer.Math. Soc. 88 (1983), no. 2, 333–337. [Crossref]
- [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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_agms-2015-0007