Any matrix $A$ can be written as $B.U$ where $B=\sqrt{AA^\top}$ is posititive semidefinite and $U$ is orthogonal (polar decomposition). Thus $|\det(A)| =|\det(B)|.|\det(U)|$ is the product off eigenvalues of $B$ which are $\ge 0$ and which are also called the singular values or s-numbers of $A$. Your max.min formula multiplies the two singular values of the Jacobian.

Any matrix $A$ can be written as $B.U$ where $B=\sqrt{AA^\top}$ is posititive semidefinite and $U$ is orthogonal (polar decomposition). Thus $|\det(A)| =|\det(B)|.|\det(U)|$ is the product of the eigenvalues of $B$ which are $\ge 0$ and which are also called the singular values or s-numbers of $A$. Your max.min formula multiplies the two singular values of the Jacobian.