Area and the inradius of lemniscates

Alexander Yu Solynin, Alexander S. Williams

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We study geometric properties of filled lemniscates E (p, c) = {z ∈ C : | p (z) | ≤ c} of a complex polynomial p (z) of degree n. In particular, we answer a question raised by H.H. Cuenya and F.E. Levis (2007) by showing that there is a constant C (n) such that frac(μ (E (p, c)), π r2 (E (p, c))) ≤ C (n) for every lemniscate E (p, c). Here μ (E (p, c)) and r (E (p, c)) denote the area and the inradius of E (p, c).

Original languageEnglish
Pages (from-to)507-517
Number of pages11
JournalJournal of Mathematical Analysis and Applications
Volume354
Issue number2
DOIs
StatePublished - Jun 15 2009

Keywords

  • Area
  • Inradius
  • Lemniscate
  • Polynomial

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