I take $F$ from $\Omega\subset \mathbb C^n$ to $\mathbb C^n$ to be a holomorphic function such that $$| \det(J_F)|\leq 1,$$ where $J_F$ is the Jacobian matrix of $F$.
My question: Is there any classification of functions of this type?
Holomorphic function on $\mathbb C^n$
Said Kamam
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