Diameter, width and thickness of spherical reduced convex bodies with an application to Wulff shapes

摘要

After a few claims about lunes and convex sets on the d-dimensional sphere Sddocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$S<^>d$$end{document} we present some relationships between the diameter, width and thickness of reduced convex bodies and bodies of constant diameter on Sddocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$S<^>d$$end{document}. These relationships are applied for proving the final theorem, which permits to recognize if a Wulff shape in the Euclidean space is self-dual.