- #1
Bacle
- 662
- 1
Hi, Everyone:
Say f(z) defined on a region R , is a complex-analytic bijection. Does it follow
that f:R--->f(R) is a diffeomorphism, i.e., is f<sup>-1</sup> also analytic?
I know this is not true for the real-analytic case, e.g., f(x)=x<sup>3</sup> , but complex-
analytic is stronger than real-analytic ; I think this may be some corollary of
the inverse function theorem.
Any Ideas?
Say f(z) defined on a region R , is a complex-analytic bijection. Does it follow
that f:R--->f(R) is a diffeomorphism, i.e., is f<sup>-1</sup> also analytic?
I know this is not true for the real-analytic case, e.g., f(x)=x<sup>3</sup> , but complex-
analytic is stronger than real-analytic ; I think this may be some corollary of
the inverse function theorem.
Any Ideas?