On Milnor fibrations of mixed functions, a_f-condition and boundary stability

Abstract

Convenient mixed functions with strongly non-degenerate Newton boundaries have a Milnor fibration ([9]), as the isolatedness of the singularity follows from the convenience. In this paper, we consider the Milnor fibration for non-convenient mixed functions. We also study geometric properties such as Thom's a_f-condition, the transversality of the nearby fibers and stable boundary property of the Milnor fibration and their relations.