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  "body": "\n## Summary\n\nA quasiregular map is a map between domains of $\\R^n$ whose infinitesimal distortion is bounded.\nIt sends small balls to sets that are round up to a fixed factor.\nUnlike a [[quasiconformal map|SB8KG46NHP]], it need not be injective, so it generalizes holomorphic functions rather than conformal maps.\nIn the plane, quasiregular maps are holomorphic functions composed with quasiconformal homeomorphisms.\nIn dimension $n \\ge 3$ they give a rich substitute for holomorphic functions, since conformal maps there are only Möbius maps.\n\n## Explanations\n\n### L1 human\n\nA holomorphic function stretches the plane near each point by the same amount in all directions.\nA quasiregular map may stretch more in one direction than in another, but the ratio is bounded by a fixed constant at all points.\nIt may fold and cover some points several times, like $z \\mapsto z^2$.\nResults of Reshetnyak show that such maps, when not constant, still keep key features of holomorphic functions: they are open and their preimages of points are discrete.\n",
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