In this post
A star shaped open set in $\mathbb{R}^n$ is diffeomorphic to $\mathbb{R}^n$
I found a proof that $\Omega$ is always diffeomorphic to $\mathbb{R}^3$. In which cases can such a diffeomorphism be analytical?
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up.
Sign up to join this communityIn this post
A star shaped open set in $\mathbb{R}^n$ is diffeomorphic to $\mathbb{R}^n$
I found a proof that $\Omega$ is always diffeomorphic to $\mathbb{R}^3$. In which cases can such a diffeomorphism be analytical?
There is a general theorem (Morrey and Grauert) stating that if two real-analytic manifolds are diffeomorphic then they are real-analytically isomorphic.
H. Grauert, On Levi’s problem and the imbedding of real analytic manifolds, Ann. of Math., 68 (1958), 460-472.
C. B. Morrey, The analytic embedding of abstract real analytic manifolds, Ann. of Math., 68 (1958), 159-201.