Kquasiconformal
K-quasiconformal (often written K-quasiconformal) refers to a class of maps that generalize conformal maps by allowing controlled distortion. In the plane (and more generally in n-dimensional spaces), a sense-preserving homeomorphism f between domains is K-quasiconformal if it has locally square-integrable first derivatives and its differential distorts infinitesimal shapes by at most a factor K ≥ 1.
A common analytic formulation uses the Beltrami equation. There exists a measurable function μ with ||μ||∞ ≤ k < 1
Key properties include: K = 1 corresponds to conformal maps; the inverse of a K-quasiconformal map is
Regularity aspects include Hölder continuity with exponent 1/K in the plane, with sharpness in general. K-quasiconformal