If we have smooth embedding $\phi:s^1\rightarrow R^2$ ,how to prove that the interior $\Omega$ is smooth homoemorphism to $D^2$ .
I can prove this question use Jordan curve theorem and Riemann mapping theorem these two big theorem.But I'm trying to find a more element method and can be extend to other dimenssion. I think this question is equivalent to find a smooth function $f|_{\partial\Omega}=0$ with single maximum point and no minimum point in $\Omega$ .I have tried to use some elliptic pde method to solve this problem but I failed.