The Quantitative Isoperimetric Inequality for Planar Convex Domains

Carlo Nitsch

Bollettino dell'Unione Matematica Italiana (2008)

  • Volume: 1, Issue: 3, page 573-589
  • ISSN: 0392-4041

Abstract

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We prove that among all the convex bounded domains in ℝ 2 having an assigned Fraenkel asymmetry index, there exists only one convex set (up to a similarity) which minimizes the isoperimetric deficit. We show how to construct this set. The result can be read as a sharp improvement of the isoperimetric inequality for convex planar domains.

How to cite

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Nitsch, Carlo. "The Quantitative Isoperimetric Inequality for Planar Convex Domains." Bollettino dell'Unione Matematica Italiana 1.3 (2008): 573-589. <http://eudml.org/doc/290467>.

@article{Nitsch2008,
abstract = {We prove that among all the convex bounded domains in $\mathbb\{R\}^2$ having an assigned Fraenkel asymmetry index, there exists only one convex set (up to a similarity) which minimizes the isoperimetric deficit. We show how to construct this set. The result can be read as a sharp improvement of the isoperimetric inequality for convex planar domains.},
author = {Nitsch, Carlo},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {573-589},
publisher = {Unione Matematica Italiana},
title = {The Quantitative Isoperimetric Inequality for Planar Convex Domains},
url = {http://eudml.org/doc/290467},
volume = {1},
year = {2008},
}

TY - JOUR
AU - Nitsch, Carlo
TI - The Quantitative Isoperimetric Inequality for Planar Convex Domains
JO - Bollettino dell'Unione Matematica Italiana
DA - 2008/10//
PB - Unione Matematica Italiana
VL - 1
IS - 3
SP - 573
EP - 589
AB - We prove that among all the convex bounded domains in $\mathbb{R}^2$ having an assigned Fraenkel asymmetry index, there exists only one convex set (up to a similarity) which minimizes the isoperimetric deficit. We show how to construct this set. The result can be read as a sharp improvement of the isoperimetric inequality for convex planar domains.
LA - eng
UR - http://eudml.org/doc/290467
ER -

References

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