An Analytic Approach to The Cancellation Problem for Affine Spaces over   $\mathbb{C}$
  The Cancellation Problem for Affine Spaces is settled affirmatively, that is, it is proved that : Let $ k $ be an algebraically closed field of characteristic zero and let $n, m \in \mathbb{N}$. If $R[Y_1,..., Y_m] \cong_k k[X_1,..., X_{n+m}]$ as $k$-algebras, where $Y_1,..., Y_m, X_1,..., X_{n+m}$ are indeterminates, then $R \cong_k k[X_1,..., X_n]$. 
Susumu Oda