On the maximal dilatation of quasiconformal minimal Lagrangian extensions
Résumé
Given a quasisymmetric homeomorphism ϕ of the circle, Bonsante and Schlenker proved the existence and uniqueness of the minimal Lagrangian extension f_ϕ : H^2 → H^2 to the hyperbolic plane. By previous work of the author, its maximal dilatation satisfies log K(f_ϕ) ≤ C||ϕ||_cr, where ||ϕ||_cr denotes the cross-ratio norm. We give constraints on the value of an optimal such constant C, and discuss possible lower inequalities, by studying two one-parameter families of minimal Lagrangian extensions in terms of maximal dilatation and cross-ratio norm.
Origine | Fichiers produits par l'(les) auteur(s) |
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