Circles Minimize most Knot Energies

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dc.creatorAbrams, Aaron
dc.creatorCantarella, Jason
dc.creatorFu, Joseph H. G.
dc.creatorGhomi, Mohammad
dc.creatorHoward, Ralph
dc.date2001-05-16
dc.date.accessioned2026-07-07T04:41:44Z
dc.date.available2026-07-07T04:41:44Z
dc.descriptionWe define a new class of knot energies (known as renormalization energies) and prove that a broad class of these energies are uniquely minimized by the round circle. Most of O'Hara's knot energies belong to this class. This proves two conjectures of O'Hara and of Freedman, He, and Wang. We also find energies not minimized by a round circle. The proof is based on a theorem of G. Luko on average chord lengths of closed curves.
dc.description15 pages with 3 figures. See also http://www.math.sc.edu/~howard/
dc.identifierhttps://arxiv.org/abs/math/0105138
dc.identifierhttp://arxiv.org/abs/math/0105138
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/61483
dc.subjectGeometric Topology
dc.subjectDifferential Geometry
dc.subject53A04; 52A40
dc.titleCircles Minimize most Knot Energies
dc.typetext

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