On the scaling methods by Pinchuk and Frankel

Seungro Joo

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arXiv · 1607.06580

On the scaling methods by Pinchuk and Frankel

Seungro Joo

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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 $\mathbb{C}^2$. 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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Seungro Joo. 2016-07-22. On the scaling methods by Pinchuk and Frankel. https://arxiv.org/abs/1607.06580

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