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arXiv · 1912.09462

Minimizers of the prescribed curvature functional in a Jordan domain with no necks

Gian Paolo Leonardi·Giorgio Saracco
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Abstract

We provide a geometric characterization of the minimal and maximal minimizer of the prescribed curvature functional $P(E)-κ|E|$ among subsets of a Jordan domain $Ω$ with no necks of radius $κ^{-1}$, for values of $κ$ greater than or equal to the Cheeger constant of $Ω$. As an application, we describe all minimizers of the isoperimetric profile for volumes greater than the volume of the minimal Cheeger set, relative to a Jordan domain $Ω$ which has no necks of radius $r$, for all $r$. Finally, we show that for such sets and volumes the isoperimetric profile is convex.

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Gian Paolo Leonardi, Giorgio Saracco. 2020-05-18. Minimizers of the prescribed curvature functional in a Jordan domain with no necks. https://doi.org/10.1051/cocv%2F2020030

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