Criticality for the Gehring link problem

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dc.creatorCantarella, Jason
dc.creatorFu, Joseph H G
dc.creatorKusner, Rob
dc.creatorSullivan, John M
dc.creatorWrinkle, Nancy C
dc.date2004-02-13
dc.date2009-03-02
dc.date.accessioned2026-07-07T12:47:43Z
dc.date.available2026-07-07T12:47:43Z
dc.descriptionIn 1974, Gehring posed the problem of minimizing the length of two linked curves separated by unit distance. This constraint can be viewed as a measure of thickness for links, and the ratio of length over thickness as the ropelength. In this paper we refine Gehring's problem to deal with links in a fixed link-homotopy class: we prove ropelength minimizers exist and introduce a theory of ropelength criticality. Our balance criterion is a set of necessary and sufficient conditions for criticality, based on a strengthened, infinite-dimensional version of the Kuhn--Tucker theorem. We use this to prove that every critical link is C^1 with finite total curvature. The balance criterion also allows us to explicitly describe critical configurations (and presumed minimizers) for many links including the Borromean rings. We also exhibit a surprising critical configuration for two clasped ropes: near their tips the curvature is unbounded and a small gap appears between the two components. These examples reveal the depth and richness hidden in Gehring's problem and our natural extension.
dc.descriptionThis is the version published by Geometry & Topology on 14 November 2006
dc.identifierhttps://arxiv.org/abs/math/0402212
dc.identifierhttp://arxiv.org/abs/math/0402212
dc.identifierGeom. Topol. 10 (2006) 2055-2115
dc.identifierdoi:10.2140/gt.2006.10.2055
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/221814
dc.subjectDifferential Geometry
dc.subjectGeometric Topology
dc.subject57M25, 49Q10, 53A04
dc.titleCriticality for the Gehring link problem
dc.typetext

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