Polyhedral compactifications, I-Reference-Cited by-同舟云学术

Polyhedral compactifications, I

Published:2023-08-01 Issue:3 Volume:23 Page:413-436
ISSN:1615-7168
Container-title:Advances in Geometry
language:en
Short-container-title:

Author:

Ciobotaru Corina¹,Kramer Linus²,Schwer Petra³

Affiliation:

1. Aarhus Inst. of Advanced Studies and Department of Mathematics at Aarhus University , Hoeegh-Guldbergs Gade 6B , Aarhus C , Denmark

2. Mathematisches Institut, Univ. Münster , Einsteinstr. 62 , Münster , Germany

3. Institut für Algebra und Geometrie, Univ. Magdeburg , Universitätsplatz 2 , Magdeburg , Germany

Abstract

Abstract In this work we describe horofunction compactifications of metric spaces and finite-dimensional real vector spaces through asymmetric metrics and asymmetric polyhedral norms by means of nonstandard methods, that is, by ultrapowers of the spaces at hand. The polyhedral compactifications of the vector spaces carry the structure of stratified spaces with the strata indexed by dual faces of the polyhedral unit ball. Explicit neighborhood bases and descriptions of the horofunctions are provided.

Publisher

Walter de Gruyter GmbH

Subject

Geometry and Topology

Link

https://www.degruyter.com/document/doi/10.1515/advgeom-2023-0018/pdf

Reference31 articles.

1. J. L. Bell, A. B. Slomson, Models and ultraproducts: An introduction. North-Holland 1969. MR0269486 Zbl 0179.31402

2. C. D. Bennett, Affine Λ-buildings. I. Proc. London Math. Soc. (3) 68 (1994), 541–576. MR1262308 Zbl 0834.20026

3. C. D. Bennett, P. N. Schwer, On axiomatic definitions of non-discrete affine buildings. Adv. Geom. 14 (2014), 381–412. MR3228889 Zbl 1408.51009

4. A. Borel, L. Ji, Compactifications of symmetric and locally symmetric spaces. Birkhäuser Boston, Inc., Boston, MA 2006. MR2189882 Zbl 1100.22001

5. N. Bourbaki, Lie groups and Lie algebras. Chapters 4–6. Springer 2002. MR1890629 Zbl 0983.17001

Cited by 2 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Horofunctions and metric compactification of noncompact Hermitian symmetric spaces;Annali di Matematica Pura ed Applicata (1923 -);2024-01-24

2. Horofunction compactifications of symmetric cones under Finsler distances;Annales Fennici Mathematici;2023-11-20