Reciprocal lower bound on modulus of curve families in metric surfaces
Kai Rajala, Matthew Romney · Annales Academiae Scientiarum Fennicae Mathematica · 2019
We prove that any metric space X homeomorphic to R 2 with locally finite Hausdorff 2-measure satisfies a reciprocal lower bound on modulus of curve families associated to a quadrilateral.More precisely, let Q ⊂ X be a topological quadrilateral with boundary edges (in cyclic order) denoted by. This answers a question in [6] concerning minimal hypotheses under which a metric space admits a quasiconformal parametrization by a domain in R 2 .