Editing Cauchy–Riemann equations (section)

=== Conformal mappings in higher dimensions ===
Let Ω be an open set in the Euclidean space <math>\mathbb{R}^n</math>. The equation for an orientation-preserving mapping <math>f:\Omega\to\mathbb{R}^n</math> to be a [[conformal mapping]] (that is, angle-preserving) is that
<math display="block">Df^\mathsf{T} Df = (\det(Df))^{2/n}I</math>

where ''Df'' is the Jacobian matrix, with transpose <math>Df^\mathsf{T}</math>, and ''I'' denotes the identity matrix.{{r|IwaniecMartin2001_32}} For {{math|1=''n'' = 2}}, this system is equivalent to the standard Cauchy–Riemann equations of complex variables, and the solutions are holomorphic functions. In dimension {{math|''n'' > 2}}, this is still sometimes called the Cauchy–Riemann system, and [[Liouville's theorem (conformal mappings)|Liouville's theorem]] implies, under suitable smoothness assumptions, that any such mapping is a [[Möbius transformation]].