English

A Homogeneous Function Constant along the Leaves of a Foliation

Complex Variables 2018-07-04 v1

Abstract

Given a smooth foliation by complex curves (locally around a point xC2{0}x\in\mathbb{C}^2\setminus\{0\}) which is "compatible" with the foliation by spheres centered at the origin, we construct a smooth real-valued function gg in a neighborhood of said point, which is positive, homogeneous and constant along the leaves. A corollary we obtain from this is relevant to the problem of "bumping out" certain pseudoconvex domains in C3\mathbb{C}^3.

Keywords

Cite

@article{arxiv.1807.01199,
  title  = {A Homogeneous Function Constant along the Leaves of a Foliation},
  author = {Lars Simon},
  journal= {arXiv preprint arXiv:1807.01199},
  year   = {2018}
}

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13 pages