References
[Cla] Clarkson, J.A.: Uniformly convex spaces. Trans. Am. Math. Soc.40, 396–414 (1936)
[Cox] Coxeter, H.S.M.: Regular Polytopes. Dover New York: Dover Publications, INC 1973
[Cud] Cudia, D.F.: The geometry of Banach spaces. Smoothness. Trans. Am. Math. Soc.110, 284–314 (1964)
[Day] Day, M.M.: Uniform convexity in factor and conjugate spaces. Ann. Math.45, 375–385 (1944)
[Enf] Enflo, P.: Banach spaces which can be given an equivalent uniformly convex norm. Isr. J. Math.13, 281–289 (1972)
[Jam] James, R.C.: Uniformly non-square Banach spaces. Ann. Math.80, 542–550 (1964)
[Kle1] Klee, V.: Adjoints of projective transformations and face-figures of convex polytopes. Math. Program. Study, Ser.8, 209–216 (1978)
[Kle2] Klee, V.: Dispersed Chebyshev sets and covering by balls. Math. Ann.257, 251–260 (1981)
[Kle3] Klee, V.: Do infinite-dimensional Banach spaces admit nice tilings? Stud. Sci. Math. Hung.21, 415–427 (1986)
[KMZ] Klee, V., Maluta, E., Zanco, C.: Tiling with smooth and rotund tiles. Fundam. Math.126, 269–290 (1986)
[KT] Klee, V., Tricot, C.: Locally countable plump tilings are flat. Math. Ann.277, 315–325 (1987)
[Mac] Macbeath, A.M.: A compactness theorem for affine equivalence classes of convex regions. Can. J. Math.3, 54–61 (1951)
[Mah] Mahler, K.: Ein Übertragungsprinzip für konvexe Körper. Čas. Pěstování Mat. Fys.68, 93–102 (1939)
[Wri] Wriedt, M.: Charakterisierungen lokal uniform konvexer Mengen. Arch. Math.35, 548–553 (1980)
Author information
Authors and Affiliations
Additional information
Research of the first author was supported in part by the U.S. National Science Foundation. Research of the second and third authors was supported in part by the Consiglio Nazionale delle Ricerche and the Ministero dell'Università e della Ricerca Scientifica of Italy
Rights and permissions
About this article
Cite this article
Klee, V., Maluta, E. & Zanco, C. Uniform properties of collections of convex bodies. Math. Ann. 291, 153–177 (1991). https://doi.org/10.1007/BF01445197
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01445197