Minimizers of the prescribed curvature functional in a Jordan domain with no necks
| العنوان: | Minimizers of the prescribed curvature functional in a Jordan domain with no necks |
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| المؤلفون: | Gian Paolo Leonardi, Giorgio Maria Saracco |
| سنة النشر: | 2019 |
| مصطلحات موضوعية: | Pure mathematics, Control and Optimization, prescribed mean curvature, Characterization (mathematics), Curvature, 01 natural sciences, Domain (mathematical analysis), Mathematics - Analysis of PDEs, FOS: Mathematics, Mathematics::Metric Geometry, 0101 mathematics, Mathematics, Perimeter minimizer, 010102 general mathematics, Regular polygon, Cheeger constant, Radius, Cheeger constant (graph theory), 010101 applied mathematics, 49Q10, 35J93, 49Q20, Computational Mathematics, Control and Systems Engineering, Mathematics::Differential Geometry, Isoperimetric inequality, Analysis of PDEs (math.AP) |
| الوصف: | We provide a geometric characterization of the minimal and maximal minimizer of the prescribed curvature functional $P(E)-\kappa |E|$ among subsets of a Jordan domain $\Omega$ with no necks of radius $\kappa^{-1}$, for values of $\kappa$ greater than or equal to the Cheeger constant of $\Omega$. 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 $\Omega$ which has no necks of radius $r$, for all $r$. Finally, we show that for such sets and volumes the isoperimetric profile is convex. Comment: 24 pages, 4 figures |
| اللغة: | English |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::cdeafa7a0a8fb2e203a0707f635f9676 http://arxiv.org/abs/1912.09462 |
| Rights: | OPEN |
| رقم الانضمام: | edsair.doi.dedup.....cdeafa7a0a8fb2e203a0707f635f9676 |
| قاعدة البيانات: | OpenAIRE |
| الوصف غير متاح. |