We give a characterization of convex hypersurfaces with an equichordal point in terms of hedgehogs of constant width.
@article{bwmeta1.element.bwnjournal-article-apmv67z3p285bwm, author = {Yves Martinez-Maure}, title = {Hedgehogs of constant width and equichordal points}, journal = {Annales Polonici Mathematici}, volume = {66}, year = {1997}, pages = {285-288}, zbl = {0926.52006}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv67z3p285bwm} }
Yves Martinez-Maure. Hedgehogs of constant width and equichordal points. Annales Polonici Mathematici, Tome 66 (1997) pp. 285-288. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv67z3p285bwm/
[000] [1] W. Blaschke, H. Rothe und R. Weitzenböck, Aufgabe 552, Arch. Math. Phys. 27 (1917), 82.
[001] [2] M. Fujiwara, Über die Mittelkurve zweier geschlossenen konvexen Kurven in Bezug auf einen Punkt, Tôhoku Math. J. 10 (1916), 99-103. | Zbl 46.1117.01
[002] [3] P. J. Kelly, Curves with a kind of constant width, Amer. Math. Monthly 64 (1957), 333-336. | Zbl 0080.15602
[003] [4] V. Klee, Can a plane convex body have two equichordal points?, Amer. Math. Monthly 76 (1969), 54-55.
[004] [5] V. Klee, Some unsolved problems in plane geometry, Math. Mag. 52 (3) (1979), 131-145. | Zbl 0418.51005
[005] [6] R. Langevin, G. Levitt et H. Rosenberg, Hérissons et multihérissons ( Enveloppes paramétrées par leur application de Gauss), in: Singularities (Warsaw, 1985), Banach Center Publ. 20, PWN, Warszawa, 1988, 245-253. | Zbl 0658.53004
[006] [7] Y. Martinez-Maure, Sur les hérissons projectifs (enveloppes paramétrées par leur application de Gauss), Bull. Sci. Math., to appear.
[007] [8] C. M. Petty and J. M. Crotty, Characterization of spherical neighborhoods, Canad. J. Math. 22 (1970), 431-435. | Zbl 0195.12603
[008] [9] R. Schneider, Convex Bodies: The Brunn-Minkowski Theory, Cambridge Univ. Press, 1993. | Zbl 0798.52001
[009] [10] E. Wirsing, Zur Analytizität von Doppelspeichkurven, Arch. Math. (Basel) 9 (1958), 300-307. | Zbl 0083.38404