- Thread starter
- #1

constant in U. I'm trying to show that

1)f must be constant in U.

2) the essential property of the disc U that it used here

3) an example of an open set U for which the conclusion fails.

Let f=u+vi where u is a constant.Since f is holomorphic by the Cauchy–Riemann equations->

u_x=v_y and u_y=-v_x but since u is a constant u_x=u_y=0 => 0=v_y =-v_x...therefore f is constant.

The disc U has to be open,as in:U(a,r)={z:|z-a|<r}.

Is this correct?What should I do for the last part?

Thank you