Finding an equation to a function

Question

I can think of a visual example s.t. f in $\mathbf C^2$ ($\mathbf R^2$) has a single local minimum stationary point that is not a global minimum but I can't give it a concrete equation... If anyone can think of a better example (i.e. one with a simpler equation) that would be even better! Thanks.

Answer 1

How about just subtracting a Gaussian from an exponential, e.g.

$$f(x) = e^y - \frac 3 4 e^{-x^2-y^2}$$