We investigate a Besicovitch-Danzer-type characterization of a circle in a class of compact sets whose boundary divides the plane into several components.
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A. S. Besicovitch, “A problem on a circle,” J. London Math. Soc., 36, 241–244 (1961).
L. W. Danzer, “A characterization of the circle,” in: Convexity: Proceedings of the Symposium in Pure Mathematics, American Mathematical Society, Providence, RI (1963), pp. 99–100.
T. Zamfirescu, “An infinitesimal version of the Besicovitch-Danzer characterization of the circle,” Geom. Dedic., 27, 209–212 (1988).
K. von Leichtweiss, Konvexe Mengen, VEB Deuscher Verlag der Wissenschaften, Berlin (1980).
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Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 60, No. 6, pp. 862–864, June, 2008.
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Tkachuk, M.V. Besicovitch-Danzer-type characterization of a circle. Ukr Math J 60, 1009–1011 (2008). https://doi.org/10.1007/s11253-008-0096-6
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DOI: https://doi.org/10.1007/s11253-008-0096-6