The DNA Inequality in Non-Convex Regions
| dc.creator | Larson, Eric | |
| dc.date | 2008-01-13 | |
| dc.date | 2009-04-08 | |
| dc.date.accessioned | 2026-07-07T13:00:58Z | |
| dc.date.available | 2026-07-07T13:00:58Z | |
| dc.description | 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 any 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. | |
| dc.description | Versions 7--9 contains more figures, a summary of the proof, and other modifications. Version 6 has corrected a couple of minor notational problems with version 5. Versions 5--9 are (the same) major generalization of the theorem proved in versions 1--4 | |
| dc.identifier | https://arxiv.org/abs/0801.1929 | |
| dc.identifier | http://arxiv.org/abs/0801.1929 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/226011 | |
| dc.subject | Metric Geometry | |
| dc.subject | 51F99 | |
| dc.title | The DNA Inequality in Non-Convex Regions | |
| dc.type | text |