Abstract
Abstract A simple plane closed curve Γ satisfies the DNA Inequality if the average curvature of any closed curve contained inside Γ exceeds the average curvature of Γ. In 1997 Lagarias and Richardson proved that all convex curves satisfy the DNA Inequality and asked whether this is true for some non-convex curve. They conjectured that the DNA Inequality holds for certain L-shaped curves. In this paper, we disprove this conjecture for all L-shapes and construct a large class of non-convex curves for which the DNA Inequality holds. We also give a polynomial-time procedure for determining whether any specific curve in a much larger class satisfies the DNA Inequality.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
