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.
Keywords: Perimeter minimizer, prescribed mean curvature, Cheeger constant
@article{COCV_2020__26_1_A76_0,
author = {Leonardi, Gian Paolo and Saracco, Giorgio},
title = {Minimizers of the prescribed curvature functional in a {Jordan} domain with no necks},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
year = {2020},
publisher = {EDP Sciences},
volume = {26},
doi = {10.1051/cocv/2020030},
mrnumber = {4156828},
zbl = {1459.49029},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2020030/}
}
TY - JOUR AU - Leonardi, Gian Paolo AU - Saracco, Giorgio TI - Minimizers of the prescribed curvature functional in a Jordan domain with no necks JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2020 VL - 26 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2020030/ DO - 10.1051/cocv/2020030 LA - en ID - COCV_2020__26_1_A76_0 ER -
%0 Journal Article %A Leonardi, Gian Paolo %A Saracco, Giorgio %T Minimizers of the prescribed curvature functional in a Jordan domain with no necks %J ESAIM: Control, Optimisation and Calculus of Variations %D 2020 %V 26 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/cocv/2020030/ %R 10.1051/cocv/2020030 %G en %F COCV_2020__26_1_A76_0
Leonardi, Gian Paolo; Saracco, Giorgio. Minimizers of the prescribed curvature functional in a Jordan domain with no necks. ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 76. doi: 10.1051/cocv/2020030
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Cité par Sources :
G. P. L. and G. S. have been partially supported by the INdAM-GNAMPA Project 2019 “Problemi isoperimetrici in spazi Euclidei e non” (n. prot. U-UFMBAZ-2019-000473 11-03-2019).
