On exotic algebraic structures on affine spaces

We review the recent developement on the subject, emphasizing its analytic aspects and pointing out some open problems. The study of exotic C-s is at the very beginning, and hopefully this survey would be useful to learn more about these unusual and beautiful objects. All algebraic varieties considered below are usually assumed being smooth, reduced, irreducible, and defined over C. Isomorphism means biregular isomorphism of algebraic varieties and is denoted by ≃. It is my pleasure to thank Sh. Kaliman and P. Russell. Without their friendly help and advice this survey would not be written.