*The principle curvatures of a randomly projected (Gaussian) surface are weighted averages of the principle curvatures of the original surface (with Chi-square coefficients)*

So: non-convexity in the projected surface

\(\Longleftrightarrow\) non-positive projected Hessian eigenvalues

\(\Longrightarrow\) non-positive original Hessian eigenvalues

\(\Longleftrightarrow\) non-convexity in original surface