On C2-smooth Surfaces of Constant Width.

Guilfoyle, Brendan; Klingenberg, Wilhelm

Abstract

In this paper, we obtain a number of results for C2-smooth surfaces of constant width in Euclidean 3-space E3-. In particular, we establish an integral inequality for constant width surfaces. This is used to prove that the ratio of volume to cubed width of a constant width surface is reduced by shrinking it along its normal lines. We also give a characterization of surfaces of constant width that have rational support function. Our techniques, which are complex differential geometric in nature, allow us to construct explicit smooth surfaces of constant width in E3, and their focal sets. They also allow for easy construction of tetrahedrally symmetric surfaces of constant width.

Citation

Guilfoyle, B., & Klingenberg, W. (2009). On C2-smooth Surfaces of Constant Width. Tbilisi Mathematical Journal, 2, 1-17

• Journal Article Type: Article
• Publication Date: 2009
• Deposit Date: Mar 7, 2011
• Journal: Tbilisi Mathematical Journal
• Print ISSN: 1875-158X
• Electronic ISSN: 1512-0139
• Publisher: De Gruyter
• Peer Reviewed: Peer Reviewed
• Volume: 2
• Pages: 1-17
• Public URL: https://durham-repository.worktribe.com/output/1511729
• Publisher URL: http://www.tcms.org.ge/Journals/TMJ/Volume2/Xpapers/tmj2_1.nohyperref.pdf