Distortion measures how a mapping changes distances or geometric quantities relative to their original values. For an injective map between metric spaces, one multiplicative measure is the product of its Lipschitz constant and the Lipschitz constant of its inverse on the image. Subgroup distortion instead compares intrinsic and ambient word metrics through a growth function.
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In mathematics, the term "distortion" can refer to various concepts depending on the context, but it generally relates to how much a mathematical object does not preserve certain properties when it is transformed or mapped in some way. Here are a few contexts in which distortion is relevant: 1. **Geometry**: In geometry, distortion can refer to the way lengths, angles, and areas are altered under various mappings or transformations.