Fengfan XIE , Yong YANG . THE CONVEX SETS OF CONSTANT WIDTH CONSTRUCTED FROM OPPOSITE SECTORS[J]. Acta mathematica scientia, Series B, 2025 , 45(1) : 118 -125 . DOI: 10.1007/s10473-025-0109-7

[1] Barbier E. Note sur le probleme de l'aiguille et el jeu du joint courvert. J Math Pure Appl, 1886, 5: 273-286
[2] Blaschke W. Konvexe Bereiche gegebener konstanter Breite und kleinsten inhalts. Math Ann, 1915, 76: 504-513
[3] Fujiwara M, Kakeya S. On some problems of maxima and minima for the curve of constant breadth and the in-resolvable curve of the equilateral triangle. Tohoku Math J, 1917, 11: 92-110
[4] Hammer P C. Constant breath curves in the plane. Proc Amer Math Soc, 1955, 6: 333-334
[5] Rosenthal A, Szasz O. Konvexe Eine Extremaleigenschaft der Kurven konstanter Breite. Jahrb Dtsch Math Verein, 1916, 25: 278-282
[6] Hsiung C C. A First Course in Differential Geometry. New York: John Willey and Sons, 1981
[7] Lay S R. Convex Sets and Their Application. New York: John Willey and Sons, 1982
[8] Pan S L. An application of the polar tangential coordinate. Journal of East China Normal University (Natural Science), 2003, 1: 13-16
[9] Martini H, Mustafaev Z. A new construction of curves of constant width. Computer Aided Geometric Design, 2008, 25: 751-755
[10] Lachand-Robert T, Qudet E. Bodies of constant width in arbitrary dimension. Mathematische Nachrichten, 2007, 280: 740-750
[11] Xu W X, Zhou J Z, Chen F W. On the isosceles trapezolds of constant with (in Chinese). Sci Sin Math, 2001, 41(10): 855-860
[12] Chakerian G D, Groemer H. Convex Bodies of Constant Width// Gruber P M, Wills J M. Convexity and Its Applications. Basel: Springer, 1983: 49-96
[13] Gardner R J. Geometric Tomography. Cambridge: Cambridge University Press, 2006
[14] Bonnesen T, Fenchel W. Theory of Convex Bodies. Moscow: BCS Associates, 1987
[15] Chen X S, Chen W H. Lectures on Differential Geometry (In Chinese). Beijing: Peking University, 2001
[16] Howard R. Convex bodies of constant width and constant brightness. Adv Math, 2006, 204: 241-261
[17] Zwierzynski M. The improved isoperimetric inequality and the wigner caustic of planar ovals. J Math Anal and Appl, 2016, 442: 726-739
[18] Bazylevych L. Hyperspace of compact bodies of constant width on sphere. Mathematical Bulletin, 2007, 4: 304-317