Let $\varphi(u,v)=(u,v,h(u,v))$ a parametrization of graph $\Gamma_h$ of $h:\mathbb{R}^2\to \mathbb{R}$ . Show that the Gaussian curvature can be expressed as $K(u,v)=\dfrac{\text{det}(Hess(h))}{(1+\|\nabla h\|^2)^2}$, where $Hess(h)$ is the Hessian matrix.
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