On the scaling methods by Pinchuk and Frankel

2016/07/22 by Joo, Seungro
#Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1607.06580

Abstract

The main purpose of this paper is to study two scaling methods developed respectively by Pinchuk and Frankel. We introduce first a continuously-varying global coordinate system, and give an alternative proof to the convergence of Pinchuk's scaling sequence (and of our modification) on bounded domains with finite type boundaries in ℂ². Using this, we discuss the modification of the Frankel scaling sequence on nonconvex domains. We also observe that two modified scalings are equivalent.

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