Relationship between subharmonic functions and gradient flow

21 Views Asked by At

Question. Let's say that $F(x,y)$ is a function with $$\frac{\partial^2 F}{\partial x^2} + \frac{\partial^2 F}{\partial y^2} \ge 0$$ everywhere (such a function is called subharmonic). What effect does the gradient flow of $F(x,y)$ have on area?