Non-convexity of extremal length
Nyckelord:
Teichmüller theory for Riemann surfaces, minimal surfaces in differential geometry, surfaces with prescribed mean curvature, harmonic functions on Riemann surfacesAbstract
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 \(\mathbb{R}^n\).Referera så här
Sagman, N. (2023). Non-convexity of extremal length. Annales Fennici Mathematici, 48(2), 691–702. https://doi.org/10.54330/afm.138339
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