| Issue |
ESAIM: COCV
Volume 26, 2020
|
|
|---|---|---|
| Article Number | 76 | |
| Number of page(s) | 20 | |
| DOI | https://doi.org/10.1051/cocv/2020030 | |
| Published online | 02 October 2020 | |
Minimizers of the prescribed curvature functional in a Jordan domain with no necks*
1
Dipartimento di Matematica,
Via Sommarive 14,
38123
Povo - Trento, Italy.
2
Dipartimento di Matematica,
Via Ferrata 5,
27100
Pavia - Pavia, Italy.
** Corresponding author: giorgio.saracco@unipv.it
Received:
20
December
2019
Accepted:
13
May
2020
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.
Mathematics Subject Classification: 49Q10 / 35J93 / 49Q20
Key words: Perimeter minimizer / prescribed mean curvature / Cheeger constant
© EDP Sciences, SMAI 2020
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