Polyhedral compactifications, I

References

[1] J. L. Bell, A. B. Slomson, Models and ultraproducts: An introduction. North-Holland 1969. MR0269486 Zbl 0179.31402Search in Google Scholar

[2] C. D. Bennett, Affine Λ-buildings. I. Proc. London Math. Soc. (3) 68 (1994), 541–576. MR1262308 Zbl 0834.2002610.1112/plms/s3-68.3.541Search in Google Scholar

[3] C. D. Bennett, P. N. Schwer, On axiomatic definitions of non-discrete affine buildings. Adv. Geom. 14 (2014), 381–412. MR3228889 Zbl 1408.5100910.1515/advgeom-2014-0017Search in Google Scholar

[4] A. Borel, L. Ji, Compactifications of symmetric and locally symmetric spaces. Birkhäuser Boston, Inc., Boston, MA 2006. MR2189882 Zbl 1100.2200110.4310/jdg/1146169912Search in Google Scholar

[5] N. Bourbaki, Lie groups and Lie algebras. Chapters 4–6. Springer 2002. MR1890629 Zbl 0983.1700110.1007/978-3-540-89394-3Search in Google Scholar

[6] M. R. Bridson, A. Haefliger, Metric spaces of non-positive curvature, volume 319 of Grundlehren der mathematischen Wissenschaften. Springer 1999. MR1744486 Zbl 0988.5300110.1007/978-3-662-12494-9Search in Google Scholar

[7] B. Brill, Eine Familie von Kompaktifizierungen affine Gebäude. PhD thesis, Frankfurt, 2006.Search in Google Scholar

[8] C. Charignon, Compactifications polygonales d’un immeuble affine. Preprint 2009, arXiv:0903.0502v1 [math.GR]Search in Google Scholar

[9] C. Ciobotaru, L. Kramer, P. Schwer, Polyhedral compactifications, II. In preparation.Search in Google Scholar

[10] J. Dugundji, Topology. Allyn and Bacon, Inc., Boston, Mass. 1966. MR0193606 Zbl 0144.21501Search in Google Scholar

[11] W. Fulton, Introduction to toric varieties, volume 131 of Annals of Mathematics Studies. Princeton Univ. Press 1993. MR1234037 Zbl 0813.1403910.1515/9781400882526Search in Google Scholar

[12] M. Gromov, Hyperbolic manifolds, groups and actions. In: Riemann surfaces and related topics: Proceedings of the 1978 Stony Brook Conference (State Univ. New York, Stony Brook, N.Y., 1978), volume 97 of Ann. of Math. Stud., 183–213, Princeton Univ. Press 1981. MR624814 Zbl 0467.5303510.1515/9781400881550-016Search in Google Scholar

[13] Y. Guivarc’h, L. Ji, J. C. Taylor, Compactifications of symmetric spaces. Birkhäuser Boston, Inc., Boston, MA 1998. MR1633171 Zbl 1053.31006Search in Google Scholar

[14] A. W. Gutiérrez, The horofunction boundary of finite-dimensional ℓ_p spaces. Colloq. Math. 155 (2019), 51–65. MR3887188 Zbl 1415.5101510.4064/cm7320-3-2018Search in Google Scholar

[15] T. Haettel, A. Schilling, C. Walsh, A. Wienhard, Horofunction compactifications of symmetric spaces. Preprint 2017, arXiv:1705.05026v2 [math.DG]Search in Google Scholar

[16] P. Hitzelberger, Generalized affine buildings: Automorphisms, affine Suzuki–Ree-buildings and convexity. PhD thesis, Münster, 2009, arXiv:0902.1107v1 [math.MG]Search in Google Scholar

[17] L. Ji, A. Schilling, Polyhedral horofunction compactification as polyhedral ball. Preprint 2016, arXiv:1607.00564v2 [math.GT]Search in Google Scholar

[18] L. Ji, A.-S. Schilling, Toric varieties vs. horofunction compactifications of polyhedral norms. Enseign. Math. 63 (2017), 375–401. MR3852176 Zbl 1402.1406510.4171/LEM/63-3/4-6Search in Google Scholar

[19] M. Kapovich, B. Leeb, Finsler bordifications of symmetric and certain locally symmetric spaces. Geom. Topol. 22 (2018), 2533–2646. MR3811766 Zbl 1417.5305810.2140/gt.2018.22.2533Search in Google Scholar

[20] A. Karlsson, V. Metz, G. A. Noskov, Horoballs in simplices and Minkowski spaces. Int. J. Math. Math. Sci. 2006, Art. ID 23656, 20 pages. MR2268510 Zbl 1144.5201610.1155/IJMMS/2006/23656Search in Google Scholar

[21] J. L. Kelley, I. Namioka, Linear topological spaces. Springer 1976. MR0394084 Zbl 0318.46001Search in Google Scholar

[22] B. Kleiner, B. Leeb, Rigidity of quasi-isometries for symmetric spaces and Euclidean buildings. Inst. Hautes Études Sci. Publ. Math. 86 (1997), 115–197 (1998). MR1608566 Zbl 0910.5303510.1007/BF02698902Search in Google Scholar

[23] L. Kramer, R. M. Weiss, Coarse equivalences of Euclidean buildings. Adv. Math. 253 (2014), 1–49. MR3148544 Zbl 1327.5101510.1016/j.aim.2013.10.031Search in Google Scholar

[24] E. Landvogt, A compactification of the Bruhat-Tits building. Springer 1996. MR1441308 Zbl 0935.2003410.1007/BFb0094594Search in Google Scholar

[25] B. Rémy, A. Thuillier, A. Werner, Bruhat-Tits theory from Berkovich’s point of view. II Satake compactifications of buildings. J. Inst. Math. Jussieu 11 (2012), 421–465. MR2905310 Zbl 1241.5100310.1017/S1474748011000168Search in Google Scholar

[26] A. Robinson, Introduction to model theory and to the metamathematics of algebra. North-Holland 1963. MR0153570 Zbl 0118.25302Search in Google Scholar

[27] R. T. Rockafellar, R. J.-B. Wets, Variational analysis, volume 317 of Grundlehren der mathematischen Wissenschaften. Springer 1998. MR1491362 Zbl 0888.4900110.1007/978-3-642-02431-3Search in Google Scholar

[28] H. H. Schaefer, Topological vector spaces. Springer 1971. MR0342978 Zbl 0217.1600210.1007/978-1-4684-9928-5Search in Google Scholar

[29] P. N. Schwer, K. Struyve, Λ-buildings and base change functors. Geom. Dedicata 157 (2012), 291–317. MR2893490 Zbl 1267.5101010.1007/s10711-011-9611-2Search in Google Scholar

[30] C. Walsh, The horofunction boundary of finite-dimensional normed spaces. Math. Proc. Cambridge Philos. Soc. 142 (2007), 497–507. MR2329698 Zbl 1163.5304810.1017/S0305004107000096Search in Google Scholar

[31] A. Werner, Compactifications of Bruhat-Tits buildings associated to linear representations. Proc. Lond. Math. Soc. (3) 95 (2007), 497–518. MR2352569 Zbl 1131.2001910.1112/plms/pdm019Search in Google Scholar