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Complete sets, radii, and inner radii

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Abstract

In this paper we discuss some properties concerning sets of constant width and some related classes of sets. In particular, we discuss for such sets radii, self radii, and the existence of centers and incenters. By means of several examples, some of them rather pathological, we try to sketch a fairly complete picture concerning the different situations that are possible and their implications.

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References

  • Astaneh A.A.: Inscribed centers, reflexivity, and some applications. J. Aust. Math. Soc., Series A 41, 317–324 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  • Aumann G.: Inequalities for curves of constant breadth. J. Geom. 31, 6–21 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  • Baronti M., Casini E., Papini P.L.: Equilateral sets and their central points. Rend. Mat. Appl. 13(7), 133–148 (1993)

    MATH  MathSciNet  Google Scholar 

  • Baronti M., Papini P.L.: Diameters, centers and diametrically maximal sets. Rend. Circ. Mat. Palermo Suppl. 38(2), 11–24 (1995)

    MathSciNet  Google Scholar 

  • Brandenberg R., Dattasharma A., Gritzmann P., Larman D.: Isoradial bodies. Discret. Comput. Geom. 32, 447–457 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  • Cabello Pinar J.C.: Convexos de anchura constante en dimension infinita. Actas Jornadas Hispano-Lusas, Valladolid (1988)

    Google Scholar 

  • Chakerian G.D., Groemer H.: Convex bodies of constant width. In: Gruber, P.M., Wills, J.M. (eds) Convexity and its Applications, pp. 49–96. Birkhäuser, Basel (1983)

    Google Scholar 

  • Heil, E., Martini, H.: Special convex bodies. In: Gruber, P.M., Wills, J.M. (eds) Handbook of Convex Geometry, Vol. A, North-Holland Publ. Co., 347–385 (1993)

  • Hernández Cifre M.H., Salinas G., Segura Gomis S.: Two optimization problems for convex bodies in the n-dimensional space. Beitr. Algebra Geom. 45, 549–555 (2004)

    MATH  Google Scholar 

  • Martini H., Swanepoel K.J.: The geometry of Minkowski spaces—a survey, Part II. Expo. Math. 22, 93–144 (2004)

    MATH  MathSciNet  Google Scholar 

  • Moreno J.P., Papini P.L., Phelps R.R.: New families of convex sets related to diametral maximality. J. Convex. Anal. 13, 823–837 (2006)

    MATH  MathSciNet  Google Scholar 

  • Sallee G.T.: Sets of constant width, the spherical intersection property and circumscribed balls. Bull. Aust. Math. Soc. 33, 369–371 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  • Thompson, A.C.: Minkowski Geometry. Encycl. Math. Appl. Vol. 63, Cambridge University Press, Cambridge (1966)

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Authors and Affiliations

  1. Dipartimento di Matematica “F. Enriques”, Università degli Studi di Milano, Via Saldini, 50, 20133, Milano, Italy

    Luigi Caspani

  2. Dipartimento di Matematica, Università di Bologna, Piazza Porta S. Donato, 5, 40126, Bologna, Italy

    Pier Luigi Papini

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  1. Luigi Caspani
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  2. Pier Luigi Papini
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Correspondence to Pier Luigi Papini.

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Caspani, L., Papini, P.L. Complete sets, radii, and inner radii. Beitr Algebra Geom 52, 163–170 (2011). https://doi.org/10.1007/s13366-011-0014-1

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  • DOI: https://doi.org/10.1007/s13366-011-0014-1

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