Reciprocal lower bound on modulus of curve families in metric surfaces

DOI10.5186/aasfm.2019.4442zbMath1422.30080arXiv1801.08223OpenAlexW2963025454WikidataQ109747214 ScholiaQ109747214MaRDI QIDQ5224328

Kai Rajala, Matthew Romney

Publication date: 23 July 2019

Published in: Annales Academiae Scientiarum Fennicae Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1801.08223

zbMATH Keywords

uniformizationquasiconformal mappingconformal moduluscoarea inequality

Mathematics Subject Classification ID

Quasiconformal mappings in (mathbb{R}^n), other generalizations (30C65) Length, area, volume, other geometric measure theory (28A75) Quasiconformal mappings in metric spaces (30L10)

Related Items (7)

On the sharp lower bound for duality of modulus ⋮ Coarea inequality for monotone functions on metric surfaces ⋮ Quasiconformal geometry and removable sets for conformal mappings ⋮ Monotone Sobolev functions in planar domains: level sets and smooth approximation ⋮ Uniformization with infinitesimally metric measures ⋮ A sharp necessary condition for rectifiable curves in metric spaces ⋮ Quasiconformal Jordan domains

Cites Work

• Uniformization of two-dimensional metric surfaces
• Quasisymmetric parametrizations of two-dimensional metric spheres
• Lectures on analysis on metric spaces
• Good metric spaces without good parameterizations
• Finding curves on general spaces through quantitative topology, with applications to Sobolev and Poincaré inequalities
• Quasiconformal parametrization of metric surfaces with small dilatation
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