Some weighted isoperimetric inequalities in quantitative form

Nicola Fusco; Domenico Angelo La Manna

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arXiv · 2207.06250

Some weighted isoperimetric inequalities in quantitative form

Nicola Fusco·Domenico Angelo La Manna

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Abstract

In this paper we study two different weighted isoperimetric inequalities. In the first part of the paper we prove a sharp stability result for the isoperimetric inequality with a log-convex weight. In the second part we analize the behavior of a negative power weight for the perimeter thus providing a complete picture of the isoperimetric problem in this context.

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Nicola Fusco, Domenico Angelo La Manna. 2022-07-13. Some weighted isoperimetric inequalities in quantitative form. https://arxiv.org/abs/2207.06250

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