Nonlocal perimeter, curvature and minimal surfaces for measurable sets

DOI10.1007/s11854-019-0027-5zbMath1426.49043OpenAlexW2945502287WikidataQ127577546 ScholiaQ127577546MaRDI QIDQ2330783

Julián Toledo, Julio D. Rossi, José M. Mazón Ruiz

Publication date: 23 October 2019

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11854-019-0027-5

zbMATH Keywords

isoperimetric inequalitymean curvatureminimal surfaceskernelperimeter\(J\)-calibrable sets

Mathematics Subject Classification ID

Minimal surfaces and optimization (49Q05) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Fractional derivatives and integrals (26A33) Fractional partial differential equations (35R11)

Related Items (17)

Gradient flows in metric random walk spaces ⋮ Fractional total variation denoising model with \(L^1\) fidelity ⋮ \((\mathrm{BV},L^p)\)-decomposition, \(p = 1,2\), of functions in metric random walk spaces ⋮ The Cheeger cut and Cheeger problem in metric graphs ⋮ Asymptotics of non-local perimeters ⋮ Local Hölder regularity of minimizers for nonlocal variational problems ⋮ The Cheeger cut and Cheeger problem in metric measure spaces ⋮ On the solutions of nonlocal 1-Laplacian equation with \(L^1\)-data ⋮ Calibrations and null-Lagrangians for nonlocal perimeters and an application to the viscosity theory ⋮ The Dirichlet random walk ⋮ Torsional Rigidity in Random Walk Spaces ⋮ The Cheeger problem in abstract measure spaces ⋮ An isoperimetric problem with a competing nonlocal singular term ⋮ The total variation flow in metric random walk spaces ⋮ Convergence of nonlocal geometric flows to anisotropic mean curvature motion ⋮ Local minimizers and gamma-convergence for nonlocal perimeters in Carnot groups ⋮ (Dis)connectedness of nonlocal minimal surfaces in a cylinder and a stickiness property

Cites Work

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• Two subtle convex nonlocal approximations of the BV-norm
• Regularity of nonlocal minimal cones in dimension 2
• The fractional Cheeger problem
• A new approach to Sobolev spaces and connections to \(\Gamma\)-convergence
• Uniform estimates and limiting arguments for nonlocal minimal surfaces
• Gamma-convergence of nonlocal perimeter functionals
• Convergence of nonlocal threshold dynamics approximations to front propagation
• A nonlocal \(p\)-Laplacian evolution equation with Neumann boundary conditions
• The limit as \(p \rightarrow \infty \) in a nonlocal \(p\)-Laplacian evolution equation: a nonlocal approximation of a model for sandpiles
• Level set approach for fractional mean curvature flows
• Functional analysis, Sobolev spaces and partial differential equations
• Generalized coarea formula and fractal sets
• On an open question about functions of bounded variation.
• Parabolic quasilinear equations minimizing linear growth functionals
• An estimate in the spirit of Poincaré's inequality
• A characterization of convex calibrable sets in \(\mathbb R^N\)
• A fractional framework for perimeters and phase transitions
• New approximations of the total variation and filters in imaging
• The first eigenvalue of the Laplacian, isoperimetric constants, and the max flow min cut theorem
• BMO-Type Norms Related to the Perimeter of Sets
• Geometric Analysis of Fractional Phase Transition Interfaces
• A Notion of Nonlocal Curvature
• Nonlocal Operators with Applications to Image Processing
• Nonconvex Functionals Related to Multiphase Systems
• Fundamentals of Non-Local Total Variation Spectral Theory
• A Nonlocalp-Laplacian Evolution Equation with Nonhomogeneous Dirichlet Boundary Conditions
• Nonlocal minimal surfaces
• Uniqueness of the Cheeger set of a convex body

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