Harmonic Univalent Mappings and Linearly Connected Domains

Details Harmonic Univalent Mappings and Linearly Connected Domains Harmonic Univalent Mappings and Linearly Connected Domains

2006-07-03

arxiv.org/abs/math/0607068v1

Mathematics

Complex Variables

Scientific paper

We investigate the relationship between the univalence of $f$ and of $h$ in the decomposition $f=h+\bar{g}$ of a sense-preserving harmonic mapping defined in the unit disk $\mathbb{D}\subset\mathbb{C}$. Among other results, we determine the holomorphic univalent maps $h$ for which there exists $c>0$ such that every harmonic mapping of the form $f=h+\bar{g}$ with $|g'|< c|h'|$ is univalent. The notion of a linearly connected domain appears in our study in a relevant way.

Affiliated with

Also associated with

No associations

Rating

Harmonic Univalent Mappings and Linearly Connected Domains does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Harmonic Univalent Mappings and Linearly Connected Domains, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Harmonic Univalent Mappings and Linearly Connected Domains will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-416299