Characterizing the Phragmen-Lindeloef condition for evolution on algebraic curves.

For an algebraic curve $V$ in $\C^k \times \C^n$ it is investigated when it satisfies the Phragm\'en-Lindel\"{o}f condition $\PL (\omega)$ of evolution in certain classes of ultradifferentiable functions. Necessary as well as sufficient conditions are obtained which lead to a complete characterization for curves in $\C \times \C^n$. Some examples illustrate how these results can be applied