Non-convexity of extremal length

N Sagman - arXiv preprint arXiv:2303.04471, 2023 - arxiv.org
With respect to every Riemannian metric, the Teichm\" uller metric, and the Thurston metric
on Teichm\" uller space, we show that there exist measured foliations on surfaces whose …

The extremal length systole of the cube punctured at its vertices

S Dobchies, MF Bourque - arXiv preprint arXiv:2404.00336, 2024 - arxiv.org
We prove that the extremal length systole of the cube punctured at its vertices is realized by
the 12 curves surrounding its edges and give a characterization of the corresponding …

[图书][B] Smoothings: A study of curve functionals

D Martínez-Granado - 2020 - search.proquest.com
We study functionals defined on the space of weighted multi-curves on a surface. One of the
key objects is the space of geodesic currents, ie, the closure of the space of weighted multi …