A sharp isoperimetric inequality in the plane

Angelo Alvino; Vincenzo Ferone; Carlo Nitsch

Journal of the European Mathematical Society (2011)

  • Volume: 013, Issue: 1, page 185-206
  • ISSN: 1435-9855

Abstract

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

How to cite

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Alvino, Angelo, Ferone, Vincenzo, and Nitsch, Carlo. "A sharp isoperimetric inequality in the plane." Journal of the European Mathematical Society 013.1 (2011): 185-206. <http://eudml.org/doc/277800>.

@article{Alvino2011,
abstract = {We show that among all the convex bounded domain 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 also show how to construct this set. The result can be read as a sharp improvement of the isoperimetric inequality for convex planar domain.},
author = {Alvino, Angelo, Ferone, Vincenzo, Nitsch, Carlo},
journal = {Journal of the European Mathematical Society},
keywords = {isoperimetric inequality; Bonnesen-style inequality; Fraenkel asymmetry; isoperimetric deficit; isoperimetric inequality; Bonnesen-style inequality; Fraenkel asymmetry; isoperimetric deficit},
language = {eng},
number = {1},
pages = {185-206},
publisher = {European Mathematical Society Publishing House},
title = {A sharp isoperimetric inequality in the plane},
url = {http://eudml.org/doc/277800},
volume = {013},
year = {2011},
}

TY - JOUR
AU - Alvino, Angelo
AU - Ferone, Vincenzo
AU - Nitsch, Carlo
TI - A sharp isoperimetric inequality in the plane
JO - Journal of the European Mathematical Society
PY - 2011
PB - European Mathematical Society Publishing House
VL - 013
IS - 1
SP - 185
EP - 206
AB - We show that among all the convex bounded domain 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 also show how to construct this set. The result can be read as a sharp improvement of the isoperimetric inequality for convex planar domain.
LA - eng
KW - isoperimetric inequality; Bonnesen-style inequality; Fraenkel asymmetry; isoperimetric deficit; isoperimetric inequality; Bonnesen-style inequality; Fraenkel asymmetry; isoperimetric deficit
UR - http://eudml.org/doc/277800
ER -

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