Abstract
We prove that two-dimensional convex subsets of spherical buildings are either buildings or have a center.
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References
Ballmann, W. and Brin, M.: Diameter rigidity of spherical polyhedra, Duke Math. J. 122 (1999), 597–609.
Balser, A. and Lytchak, A.: Building-like spaces, 2004, Preprint; Arxiv: {math.MG/0410437}.
Bridson, M. R. and Haefliger, A.: 1999, Metric Spaces of Non-Positive Curvature, Springer, Berlin.
Fujiwara, K., Nagano, K. and Shioya, T.: Fixed points sets of parabolic isometries of CAT(0)-spaces, 2004, Preprint; Arxiv: {math.DG/0408347}.
Kleiner, B.: The local structure of length spaces with curvature bounded above, Math. Z. 231(3) (1999), 409–456.
Kleiner, B. and Leeb, B.: Rigidity of quasi-isometries for symmetric spaces and Euclidean buildings, Inst. Hautes Études Sci. Publ. Math. 86 (1997), 115–197.
Kleiner, B. and Leeb, B.: Rigidity of invariant convex sets in symmetric spaces, 2004, Preprint; Arxiv: {math.DG/0412123}.
Lang, U. and Schroeder, V.: Jung's theorem for Alexandrov spaces of curvature bounded above, Ann. Global Anal. Geom. 15(3) (1997), 263–275.
Lytchak, A.: Rigidity of spherical buildings and joins, Geom. Funct. Anal. 15(3) (2005), to appear.
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Communicated by U. Bunke (Göttingen)
Mathematics Subject Classification (2000): 53C20.
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Balser, A., Lytchak, A. Centers of Convex Subsets of Buildings. Ann Glob Anal Geom 28, 201–209 (2005). https://doi.org/10.1007/s10455-005-7277-4
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DOI: https://doi.org/10.1007/s10455-005-7277-4