Holomorphic functions unbounded on curves of finite length
Complex Variables
2014-12-10 v1
Abstract
Given a pseudoconvex domain D in C^N, N>1, we prove that there is a holomorphic function f on D such that the lengths of paths p: [0,1]--> D along which Re f is bounded above, with p(0) fixed, grow arbitrarily fast as p(1)--> bD. A consequence is the existence of a complete closed complex hypersurface M in D such that the lengths of paths p:[0,1]--> M, with p(0) fixed, grow arbitrarily fast as p(1)-->bD.
Keywords
Cite
@article{arxiv.1412.2916,
title = {Holomorphic functions unbounded on curves of finite length},
author = {Josip Globevnik},
journal= {arXiv preprint arXiv:1412.2916},
year = {2014}
}
Comments
16 pages