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

DOI10.1051/cocv/2020030zbMath1459.49029arXiv1912.09462OpenAlexW3100752251MaRDI QIDQ5854368

Gian Paolo Leonardi, Giorgio Saracco

Publication date: 17 March 2021

Published in: ESAIM: Control, Optimisation and Calculus of Variations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1912.09462

zbMATH Keywords

Cheeger constantprescribed mean curvatureperimeter minimizer

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20) Optimization of shapes other than minimal surfaces (49Q10) Quasilinear elliptic equations with mean curvature operator (35J93)

Related Items (12)

Optimization of the anisotropic Cheeger constant with respect to the anisotropy ⋮ Complete systems of inequalities relating the perimeter, the area and the Cheeger constant of planar domains ⋮ A sufficient criterion to determine planar self-Cheeger sets ⋮ The optimal Hölder exponent in Massari's regularity theorem ⋮ Isoperimetric sets and \(p\)-Cheeger sets are in bijection ⋮ The Cheeger problem in abstract measure spaces ⋮ Cheeger sets for rotationally symmetric planar convex bodies ⋮ Total Variation Isoperimetric Profiles ⋮ Quantitative lower bounds to the Euclidean and the Gaussian Cheeger constants ⋮ Dimensional lower bounds for contact surfaces of Cheeger sets ⋮ Convergence of Level Sets in Total Variation Denoising Through Variational Curvatures in Unbounded Domains ⋮ The isoperimetric problem in 2d domains without necks

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the Cheeger sets in strips and non-convex domains
• The Cheeger constant of curved strips
• Volume-constrained minimizers for the prescribed curvature problem in periodic media
• An isoperimetric problem with density and the Hardy Sobolev inequality in \(\mathbb{R}^2\).
• Some isoperimetric inequalities on \(\mathbb{R}^N\) with respect to weights \(|x|^{\alpha}\)
• On the generalized Cheeger problem and an application to 2d strips
• Symmetric \(\kappa \)-loops.
• Some unusual comparison properties of capillary surfaces.
• The \(\varepsilon - \varepsilon^\beta\) property in the isoperimetric problem with double density, and the regularity of isoperimetric sets
• Embedded hyperspheres with prescribed mean curvature
• On the Dirichlet and Serrin problems for the inhomogeneous infinity Laplacian in convex domains: regularity and geometric results
• Total variation and Cheeger sets in Gauss space
• Existence and non existence of capillary surfaces
• Non existence and existence of capillary surfaces
• Minimal boundaries enclosing a given volume
• On the existence of capillary free surfaces in the absence of gravity
• Closed surface with prescribed mean curvature in \(\mathbb{R}^ 3\)
• Esistenza e regolarita delle ipersuperfici di curvatura media assegnata in \(R^n\)
• On the equation of surfaces of prescribed mean curvature. Existence and uniqueness without boundary conditions
• Area minimizing sets subject to a volume constraint in a convex set
• Space-filling curves
• On the Dirichlet problem for surfaces of prescribed mean curvature
• On the isoperimetric problem with double density
• The prescribed mean curvature equation in weakly regular domains
• Weighted Cheeger sets are domains of isoperimetry
• The Cheeger constant of a Jordan domain without necks
• Two examples of minimal Cheeger sets in the plane
• A characterization of convex calibrable sets in \(\mathbb R^N\)
• A discrete districting plan
• Characterization of Cheeger sets for convex subsets of the plane
• The mean curvature of a Lipschitz continuous manifold
• Sobolev and isoperimetric inequalities with monomial weights
• Sets of Finite Perimeter and Geometric Variational Problems
• Curvature Measures
• An Overview on the Cheeger Problem
• Seminar on Differential Geometry. (AM-102)
• Total Variation Isoperimetric Profiles
• On weighted isoperimetric inequalities with non-radial densities
• Isoperimetric inequalities in Euclidean convex bodies
• Connected components of sets of finite perimeter and applications to image processing
• Stable constant-mean-curvature hypersurfaces are area minimizing in small \(L^1\) neighborhoods

This page was built for publication: Minimizers of the prescribed curvature functional in a Jordan domain with no necks