volume preserving version of Moser's theorem
Solution 1:
This is false. For example, if $f$ is constant, then $f\circ\phi$ will also be constant. If $g$ is nonconstant, you won't be able to make $f\circ\phi = g$.
This is false. For example, if $f$ is constant, then $f\circ\phi$ will also be constant. If $g$ is nonconstant, you won't be able to make $f\circ\phi = g$.