2015/01/31 by Emilio Musso, Lorenzo Nicolodi
Mathematics · Physics and Astronomy · #Conformal anomaly #Conformal field theory #Conformal geometry #Conformal group #Conformal map #Conformal symmetry #Euclidean space #Extremal length #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Physics #Primary field #Pure mathematics #Quantization (signal processing) #math-ph #math.DG #math.MP #msc:53A04 #msc:53A30 #msc:53A55 #msc:53D20 #msc:58A17
paper · pdf · doi:10.4310/cag.2017.v25.n1.a7
published as Comm. Anal. Geom. 25 (2017), no. 1, 209-242 · 24 pages, 6 figures. v2: final version; minor changes in the exposition; references updated
openalex publication_date 2017/01/01 · arxiv created 2017/06/14 · arxiv updated 2017/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
By a conformal string in Euclidean space is meant a closed critical curve with non-constant conformal curvatures of the conformal arclength functional. We prove that (1) the set of conformal classes of conformal strings is in 1-1 correspondence with the rational points of the complex domain q∈C:1/2Req<1/√2,Imq>0,|q|<1/√2 and (2) any conformal class has a model conformal string, called symmetrical configuration, which is determined by three phenomenological invariants: the order of its symmetry group and its linking numbers with the two conformal circles representing the rotational axes of the symmetry group. This amounts to the quantization of closed trajectories of the contact dynamical system associated to the conformal arclength functional via Griffiths' formalism of the calculus of variations.