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

  • Marek LassakEmail author
Original Paper


After a few claims about lunes and convex sets on the d-dimensional sphere \(S^d\) we present some relationships between the diameter, width and thickness of reduced convex bodies and bodies of constant diameter on \(S^d\). These relationships are applied for proving the final theorem, which permits to recognize if a Wulff shape in the Euclidean space is self-dual.


Spherical geometry Lune Convex body Diameter Width Thickness Constant width Constant diameter Reduced body Wulff shape 

Mathematics Subject Classification

52A55 82D25 



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Copyright information

© The Managing Editors 2019

Authors and Affiliations

  1. 1.University of Science and TechnologyBydgoszczPoland

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