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arXiv · 1711.01197

On the maximal dilatation of quasiconformal minimal Lagrangian extensions

Andrea Seppi
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Abstract

Given a quasisymmetric homeomorphism $\varphi$ of the circle, Bonsante and Schlenker proved the existence and uniqueness of the minimal Lagrangian extension $f_\varphi:\mathbb{H}^2\to\mathbb{H}^2$ to the hyperbolic plane. By previous work of the author, its maximal dilatation satisfies $\log K(f_\varphi)\leq C||\varphi||$, where $||\varphi||$ 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.

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Andrea Seppi. 2017-11-03. On the maximal dilatation of quasiconformal minimal Lagrangian extensions. https://doi.org/10.1007/s10711-019-00422-8

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