Vol. 314, No. 1, 2021

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Moduli of Legendrian foliations and quadratic differentials in the Heisenberg group

Robin Timsit

Vol. 314 (2021), No. 1, 233–251
Abstract

Our aim is to prove the following result concerning moduli of curve families in the Heisenberg group. Let Ω be a domain in the Heisenberg group foliated by a family Γ of legendrian curves. Assume that there is a quadratic differential q on Ω such that every curve in Γ is a horizontal trajectory for q. Let lΓ : Ω ]0,+[ be the function that associates to a point p Ω the q-length of the leaf containing p. Then, the modulus of Γ is

M4(Γ) =Ω |q|2 (lΓ)4 dL3.

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Keywords
quadratic differentials, moduli of curve families, Legendrian foliations, Heisenberg group, spherical CR manifolds
Mathematical Subject Classification
Primary: 32G07, 32V05
Milestones
Received: 4 February 2021
Revised: 12 July 2021
Accepted: 16 July 2021
Published: 15 October 2021
Authors
Robin Timsit
Paris
France