Geometric and analytic quasiconformality in metric measure spaces

By Marshall Williams. 2010

56 citations recorded by the source corpus.

We prove the equivalence between geometric and analytic definitions of quasiconformality for a homeomorphism $f\colon X\rightarrow Y$ between arbitrary locally finite separable metric measure spaces, assuming no metric hypotheses on either space. When $X$ and $Y$ have locally $Q$-bounded geometry and $Y$ is contained in an Alexandrov space of curvature bounded above, the sharpness of our results implies that, as in the classical case, the modular and pointwise outer dilatations of $\map$ are related by $K_O(f)= \operatorname{esssup} H_O(x,f)$.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/2c1d76ba3c8f580ec11e0d2265433bee5a2375bd

How researchers see this paper

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In Applied Mathematics

1. Kai Rajala
2. Renjin Jiang
3. S. Wenger
4. A. Lytchak

In Geometry and Topology

1. Kai Rajala
2. A. Lytchak
3. S. Wenger

Citations in the corpus

• Uniformization of two-dimensional metric surfaces (2014, result): “See [6] and [60] for more general results concerning the equivalence between different definitions.”