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For algebraic surfaces, several global Phragmen-Lindelof conditions are characterized in terms of conditions on their limit varieties. This shows that the hyper- bolicity conditions that appeared in earlier geometric characterizations are redundant. The result is applied to the problem of existence of a continuous linear right inverse for constant coefficient partial differential operators in threevariables in Beurling classes of ultradifferentiable functions.

Characterization of global Phragmén–Lindelöf conditions for algebraic varieties by limit varieties only