English

The complex gradient inequality with parameter

Complex Variables 2014-06-24 v4

Abstract

We prove that given a holomorphic family of holomorphic functions with isolated singularities at zero and constant Milnor number, it is possible to obtain the gradient inequality with a uniform exponent.

Keywords

Cite

@article{arxiv.1403.7444,
  title  = {The complex gradient inequality with parameter},
  author = {Maciej P. Denkowski},
  journal= {arXiv preprint arXiv:1403.7444},
  year   = {2014}
}

Comments

A remark was added at the end and some misprints were corrected

R2 v1 2026-06-22T03:37:26.823Z