A complex-valued function is antiholomorphic when its complex conjugate is a holomorphic function. In one complex dimension it locally depends on and satisfies . A nonconstant antiholomorphic map reverses the orientation induced by the complex coordinates. Thus complex conjugating a holomorphic sphere map reverses its topological degree while preserving its Dirichlet energy.
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An antiholomorphic function is a type of complex function that is the complex conjugate of a holomorphic function. In the context of complex analysis, a function \( f(z) \), where \( z = x + iy \) (with \( x \) and \( y \) being real numbers), is called holomorphic at a point if it is complex differentiable in a neighborhood of that point.