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Abstrakty
In 1998 A. Soranzo introduced the notions of +infinity - and - infinity-chord functions (see [16]). In this paper we give an answer to the question when a convex body is determined by the values of -infinity-chord functions at chosen internal points. We also give some partial results regarding + infinity chord functions.
Słowa kluczowe
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Czasopismo
Rocznik
Tom
Strony
187--202
Opis fizyczny
Bibliogr. 19 poz., rys.
Twórcy
autor
- Department of Mathematics and Information Science Warsaw University of Technology Pl. Politechniki 1 00-661 Warsaw, Poland, sojkag@mini.pw.edu.pl
Bibliografia
- [1] L. M. Blumenthal, Theory and Applications of Distance Geometry, Oxford 1953.
- [2] A. Bogdewicz, On affine and metric lines in the space of convex bodies, Supplemento ai Rendiconti del Circolo Matematico di Palermo 70 (2002), no. II, 57-78.
- [3] A. Bogdewicz, Some metric properties of hyperspaces, Demonstratio Math. 32 (2000), 135-150.
- [4] K. Borsuk, Drei Sätze über die n-dimensionale euklidische Sphäre, Fund. Math. 20 (1933), 177-190.
- [5] K. J. Falconer, The Geometry of Fractal Sets, Cambridge University Press, 1990.
- [6] K. J. Falconer, X-ray problems for point sources, Proc. London Math. Soc. 46 (1983), 241-262.
- [7] R. J. Gardner, Chord functions of convex bodies, J. London Math. Soc. 36 (1987), 314-326.
- [8] R. J. Gardner, Geometric Tomography, Cambridge Univ. Press, 1995.
- [9] R. J. Gardner, A. Volčič, Tomography of convex and star bodies, Advances Math. 108 (1994), 367-399
- [10] V. Klee, Can a plane convex body have two equireciprocal points, Amer. Math. Monthly 76 (1969), 54-55.
- [11] G. D. Larman, G. Sójka, On the number of illuminations required to cover the boundary of a convex body in Rn, Rev. Roumaine Math. Pures Appl. 2006, 21-42.
- [12] M. Moszyńska, Selected Topics in Convex Geometry, Birkhäuser, Boston, 2006.
- [13] C. A. Rogers, Hausdorff Measures, Cambridge University Press, 1970.
- [14] R. Schneider, Convex Bodies: the Brunn-Minkowski Theory, Cambridge University Press, Cambridge, 1993.
- [15] R. Schneider, Pairs of convex bodies with unique joining metric segment, Bull. Soc. Roy. Sci., Liege 50 (1981), 5-7.
- [16] A. Soranzo, Determination of convex bodies from ±∞ -chord functions, Rend. Istit. Mat. Univ. Trieste 30 (1998), 129-139.
- [17] A. Soranzo, G. Sójka, Some results about + ∞-,−∞- and i -chord functions, Demonstratio Math. 39 (2006), 183-194.
- [18] W. Süss, Eibereiche mit ausgezeichneten Punkte; Sehnen-, Inhalts-und Umfangs-punkte, Tôhoku Math. J. 25 (II) (1925), 86-98.
- [19] A. Volčič, A tree point solution of Hammer’s X-ray problem, J. London Math. Soc. 34 (1986), 349-359.
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Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA5-0027-0037