Abstract
In this note we report on some recent developments in geometric knot theory which aims at finding links between geometric properties of a given knotted curve and its knot type. The central object of this field are so-called knot energies which are defined on closed embedded curves.
First we present three important examples of two-parameter knot energy families, namely O'Hara's energies, the (generalized) integral Menger curvature, and the (generalized) tangent- point energies.
Subsequently we outline the main steps that lead to C inf -regularity of stationary points- especially minimizers-in the non-degenerate sub-critical range of parameters.
Particular attention is devoted to the appearing parallels between these energies which, surprisingly at first glance, are quite similar from an analyst's perspective.
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