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Criticality For The Gehring Link Problem, Jason Cantarella, Joseph H.G. Fu, Robert Kusner, John M. Sullivan, Nancy C. Wrinkle
Criticality For The Gehring Link Problem, Jason Cantarella, Joseph H.G. Fu, Robert Kusner, John M. Sullivan, Nancy C. Wrinkle
Robert Kusner
In 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 …