TY - JOUR

T1 - Area and the inradius of lemniscates

AU - Solynin, Alexander Yu

AU - Williams, Alexander S.

PY - 2009/6/15

Y1 - 2009/6/15

N2 - 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).

AB - 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).

KW - Area

KW - Inradius

KW - Lemniscate

KW - Polynomial

UR - http://www.scopus.com/inward/record.url?scp=60349113062&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2009.01.012

DO - 10.1016/j.jmaa.2009.01.012

M3 - Article

AN - SCOPUS:60349113062

VL - 354

SP - 507

EP - 517

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

ER -