I have an exercice which is at a rather high level. I post it here, because I dont know the general level of the forum. But let see if I have some answers.
Let be a Jordan closed curve. Set
1) Let a regular parametrization of which is .
For , we note the rectangle and we set by :
where is the normal vector to at the point .
I have shown that if is small enough, then is a diffeomorphism and that
Now, I have to show that for \epsilon small enough,
I don't know how to do this. I know that I have to use the jacobien, the integral transformation (Multiple integral - Wikipedia, the free encyclopedia)