Area and the inradius of lemniscates

Alexander Solynin; Alexander S. Williams

Area and the inradius of lemniscates

Alexander Solynin, Alexander S. Williams

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

We study geometric properties of filled lemniscates $E(p,c)=\{z:\, |p(z)|\le c\}$ 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 $\frac{\mu(E(p,c))}{\pi r^2(E(p,c))}\le C(n)$ for every lemniscate $E(p,c)$. Here $\mu(E(p,c))$ and $r(E(p,c))$ denote the area and the inradius of $E(p,c)$.

Original language	English
Pages (from-to)	507-517
Journal	J. Math. Anal. Appl.
State	Published - Jan 2009

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title = "Area and the inradius of lemniscates",

abstract = "We study geometric properties of filled lemniscates $E(p,c)=\{z:\, |p(z)|\le c\}$ 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 $\frac{\mu(E(p,c))}{\pi r^2(E(p,c))}\le C(n)$ for every lemniscate $E(p,c)$. Here $\mu(E(p,c))$ and $r(E(p,c))$ denote the area and the inradius of $E(p,c)$.",

author = "Alexander Solynin and Williams, {Alexander S.}",

year = "2009",

month = jan,

language = "English",

pages = "507--517",

journal = "J. Math. Anal. Appl.",

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TY - JOUR

T1 - Area and the inradius of lemniscates

AU - Solynin, Alexander

AU - Williams, Alexander S.

PY - 2009/1

Y1 - 2009/1

N2 - We study geometric properties of filled lemniscates $E(p,c)=\{z:\, |p(z)|\le c\}$ 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 $\frac{\mu(E(p,c))}{\pi r^2(E(p,c))}\le C(n)$ for every lemniscate $E(p,c)$. Here $\mu(E(p,c))$ and $r(E(p,c))$ denote the area and the inradius of $E(p,c)$.

AB - We study geometric properties of filled lemniscates $E(p,c)=\{z:\, |p(z)|\le c\}$ 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 $\frac{\mu(E(p,c))}{\pi r^2(E(p,c))}\le C(n)$ for every lemniscate $E(p,c)$. Here $\mu(E(p,c))$ and $r(E(p,c))$ denote the area and the inradius of $E(p,c)$.

M3 - Article

SP - 507

EP - 517

JO - J. Math. Anal. Appl.

JF - J. Math. Anal. Appl.

ER -