Geodesic
Non-convexity of extremal length
Nathaniel Sagman1
1University of Luxembourg
Annales Fennici Mathematici, Tome 48 (2023) no. 2, pp. 691-702

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With respect to every Riemannian metric, the Teichmüller metric, and the Thurston metric on Teichmüller space, we show that there exist measured foliations on surfaces whose extremal length functions are not convex. The construction uses harmonic maps to $\mathbb{R}$-trees and minimal surfaces in $\mathbb{R}^n$.
DOI : 10.54330/afm.138339
Keywords: Teichmüller theory for Riemann surfaces, minimal surfaces in differential geometry, surfaces with prescribed mean curvature, harmonic functions on Riemann surfaces

Nathaniel Sagman  1

1 University of Luxembourg 
Nathaniel Sagman. Non-convexity of extremal length. Annales Fennici Mathematici, Tome 48 (2023) no. 2, pp. 691-702. doi: 10.54330/afm.138339
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