Internet searches haven't helped. Can you?


Let $\, f = \prod\_{i=1}^n (a\_i x + b\_i y + c\_i).$ 
Is each component of $\, f^{-1}(1)$ a convex curve?


I expect so, and can prove it for $n=2,$ but I'm hopeless beyond that. Thanks!



Is the level set of a product of affine linear functions comprised of convex curves?
fedja's solution: where $f>0$, $\log(f)$ is defined, with nonpositive Hessian. Thus $\log(f)$ is concave, hence has convex superlevel sets.


