A reverse isoperimetric inequality for convex shapes with inclusion constraint

Beniamin Bogosel

doi:10.1016/j.jmaa.2024.128636

A reverse isoperimetric inequality for convex shapes with inclusion constraint

Beniamin Bogosel

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

1 Citation (Scopus)

Abstract

The convex shape contained in a disk having prescribed area and maximal perimeter is completely characterized in terms of the area fraction. The solution is always a polygon having all but one sides equal. The lengths of the sides are characterized through explicit equations. The case of more general containing shapes is also discussed from both theoretical and numerical perspectives.

Original language	English
Article number	128636
Journal	Journal of Mathematical Analysis and Applications
Volume	540
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2024.128636
Publication status	Published - 15 Dec 2024

Keywords

Constrained optimization
Reverse isoperimetric inequalities
Shape optimization

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10.1016/j.jmaa.2024.128636

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title = "A reverse isoperimetric inequality for convex shapes with inclusion constraint",

abstract = "The convex shape contained in a disk having prescribed area and maximal perimeter is completely characterized in terms of the area fraction. The solution is always a polygon having all but one sides equal. The lengths of the sides are characterized through explicit equations. The case of more general containing shapes is also discussed from both theoretical and numerical perspectives.",

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AB - The convex shape contained in a disk having prescribed area and maximal perimeter is completely characterized in terms of the area fraction. The solution is always a polygon having all but one sides equal. The lengths of the sides are characterized through explicit equations. The case of more general containing shapes is also discussed from both theoretical and numerical perspectives.

KW - Constrained optimization

KW - Reverse isoperimetric inequalities

KW - Shape optimization

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A reverse isoperimetric inequality for convex shapes with inclusion constraint

Abstract

Keywords

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