Nondistortion of horospheres in Euclidean buildings and in symmetric spaces (Q1380492)

The nondistortion of horospheres is an important topic applied in the classification theory of metric spaces. By using the geometry of Euclidean buildings and the asymptotic cone, a necessary and sufficient condition is given here for the nondistortion of a horosphere in an Euclidean building and in a symmetric space. As an application, the theorem of \textit{A. Lubotzky, S. Mozes} and \textit{M. S. Raghunathan} [C. R. Acad. Sci., Paris, Sér. I 317, 735-740 (1993; Zbl 0786.22016)] is proved geometrically.