UPC condition with parameter for subanalytic sets

2018/04/27 by Denkowska, Anna, Denkowski, Maciej P.
#32B20 #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1804.10567

Abstract

In 1986 Pawłucki and Pleśniak introduced the notion of \sl uniformly polynomially cuspidal (UPC) sets and proved that every relatively compact and fat subanalytic subset of \Rzⁿ satisfies the UPC condition. Herein we investigate the UPC property of the sections of a relatively compact open subanalytic set E⊂\Rz^k×\Rzⁿ and we show that two of the three parameters in the UPC condition can be chosen independently of the section, while the third one depends generally on the point defining the section.

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