Exercises
[1H1] In the same hypotheses of the exercise [1GZ], we also assume that
.We decompose
as we did for . We define the function as . Let be the image of , show that and that is open.Show that is
is a diffeomorphism; and that its inverse is the map .Letβs define
. Show that .
(This exercise will be used, together with [1GB], to address constrained problems, in Section [2D5]).
Solution 1