Extremal Properties of Logarithmic Spirals

@inproceedings{Bolt2006ExtremalPO,
  title={Extremal Properties of Logarithmic Spirals},
  author={Michael Bolt},
  year={2006}
}
Loxodromic arcs are shown to be the maximizers of inversive arclength, which is invariant under Möbius transformations. Previously, these arcs were known to be extremals. The first result says that at any loxodromic arc, the inversive arclength functional is concave with respect to a non-trivial perturbation that fixes the circle elements at the endpoints. The second result says that among curves with monotone curvature that connect fixed circle elements, the loxodromic arcs uniquely maximize… CONTINUE READING

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