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
SN - 0022-247X
VL - 354
SP - 507
EP - 517
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 2
ER -