Stable \(s\)-minimal cones in \(\mathbb{R}^3\) are flat for \(s \sim 1\)

DOI10.1515/crelle-2019-0005zbMath1455.53030arXiv1710.08722OpenAlexW2939623742MaRDI QIDQ782613

Joaquim Serra, Eleonora Cinti, Xavier Cabré

Publication date: 28 July 2020

Published in: Journal für die Reine und Angewandte Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1710.08722

zbMATH Keywords

fractional Allen-Cahn equationBV estimatesfractional \(s\)-perimetersquared second fundamental formstable minimal cone

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Minimal surfaces and optimization (49Q05) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Fractional partial differential equations (35R11)

Related Items (13)

Boundary properties of fractional objects: flexibility of linear equations and rigidity of minimal graphs ⋮ Convex sets evolving by volume-preserving fractional mean curvature flows ⋮ Some perspectives on (non)local phase transitions and minimal surfaces ⋮ Nonlocal minimal graphs in the plane are generically sticky ⋮ Boundary continuity of nonlocal minimal surfaces in domains with singularities and a problem posed by Borthagaray, Li, and Nochetto ⋮ The stickiness property for antisymmetric nonlocal minimal graphs ⋮ Regularity results for nonlocal minimal surfaces ⋮ Periodic solutions of Allen-Cahn system with the fractional Laplacian ⋮ Second order expansion for the nonlocal perimeter functional ⋮ A three-dimensional symmetry result for a phase transition equation in the genuinely nonlocal regime ⋮ On higher-dimensional singularities for the fractional Yamabe problem: a nonlocal mazzeo-pacard program ⋮ On stable solutions for boundary reactions: a De Giorgi-type result in dimension \(4 + 1\) ⋮ Recent progress on stable and finite Morse index solutions of semilinear elliptic equations

Cites Work

• Unnamed Item
• Regularity of nonlocal minimal cones in dimension 2
• Some monotonicity results for minimizers in the calculus of variations
• Hitchhiker's guide to the fractional Sobolev spaces
• Nonlinear ground state representations and sharp Hardy inequalities
• Nonlocal \(s\)-minimal surfaces and Lawson cones
• Limiting embedding theorems for \(W^{s,p}\) when \(s\uparrow 1\) and applications
• Isoperimetry and stability properties of balls with respect to nonlocal energies
• Regularity and Bernstein-type results for nonlocal minimal surfaces
• Regularity properties of nonlocal minimal surfaces via limiting arguments
• Minimal varieties in Riemannian manifolds
• Nonlocal minimal surfaces
• Bootstrap regularity for integro-differential operators and its application to nonlocal minimal surfaces

This page was built for publication: Stable \(s\)-minimal cones in \(\mathbb{R}^3\) are flat for \(s \sim 1\)