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research
On the quantitative isoperimetric inequality in the plane with the barycentric distance
Authors
Chiara Bianchini
Gisella Croce
Antoine Henrot
Publication date
22 July 2021
Publisher
View
on
arXiv
Abstract
In this paper we study the following quantitative isoperimetric inequality in the plane:
λ
0
2
(
Ω
)
≤
C
δ
(
Ω
)
\lambda_0^2(\Omega) \leq C \delta(\Omega)
λ
0
2
​
(
Ω
)
≤
C
δ
(
Ω
)
where
δ
\delta
δ
is the isoperimetric deficit and
λ
0
\lambda_0
λ
0
​
is the barycentric asymmetry. Our aim is to generalize some results obtained by B. Fuglede in \cite{Fu93Geometriae}. For that purpose, we consider the shape optimization problem: minimize the ratio
δ
(
Ω
)
/
λ
0
2
(
Ω
)
\delta(\Omega)/\lambda_0^2(\Omega)
δ
(
Ω
)
/
λ
0
2
​
(
Ω
)
in the class of compact connected sets and in the class of convex sets
Similar works
Full text
Available Versions
HAL - Normandie Université
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oai:HAL:hal-02090603v2
Last time updated on 29/06/2022