Gluing Hyperconvex Metric Spaces

• Autorzy: Benjamin Miesch
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

hyperconvex spaces; injective metric spaces; strongly convex; externally hyperconvex

Kategorie tematyczne

• 51F99: None of the above, but in this section

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

Daty

otrzymano

2015-03-06

zaakceptowano

2015-05-05

online

2015-05-21

Twórcy

autor

Benjamin Miesch

• 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.

Identyfikatory

DOI

10.1515/agms-2015-0007