Quasiconformal mapping is a type of mapping between different spaces that generalizes the concept of conformal mappings. While conformal mappings preserve angles and are holomorphic (complex differentiable) in a neighborhood, quasiconformal mappings allow for some distortion but still maintain a controlled relationship between the shapes of the mapped objects. ### Key Concepts of Quasiconformal Mapping: 1. **Distortion Control**: In a quasiconformal mapping, the angle distortion is bounded.
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An orientation-preserving homeomorphism with locally weak derivatives and essentially bounded infinitesimal distortion. In holomorphic coordinates, its Beltrami coefficient satisfies , and the maximal dilatation is .