Generic existence of multiplicity-1 minmax minimal hypersurfaces via Allen-Cahn

DOI10.1007/s00526-022-02261-0zbMath1502.53093arXiv2010.15788OpenAlexW3094926825WikidataQ114017859 ScholiaQ114017859MaRDI QIDQ2144442

Costante Bellettini

Publication date: 13 June 2022

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2010.15788

zbMATH Keywords

bumpy metricmountain pass constructionvalley points

Mathematics Subject Classification ID

Minimal surfaces and optimization (49Q05) Variational problems in a geometric measure-theoretic setting (49Q20) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Variational methods for second-order elliptic equations (35J20) Semilinear elliptic equations (35J61) Semilinear parabolic equations (35K58)

Related Items (3)

Embeddedness of min-max CMC hypersurfaces in manifolds with positive Ricci curvature ⋮ The p-widths of a surface ⋮ Multiplicity‐1 minmax minimal hypersurfaces in manifolds with positive Ricci curvature

Cites Work

• Unnamed Item
• Morse index and multiplicity of \(\min\text{-}\max\) minimal hypersurfaces
• Min-max hypersurface in manifold of positive Ricci curvature
• A viscosity method in the min-max theory of minimal surfaces
• On stable critical points for a singular perturbation problem
• Generation and propagation of interfaces for reaction-diffusion equations
• Curvature estimates for minimal hypersurfaces
• Convergence of the Allen-Cahn equation to Brakke's motion by mean curvature
• The Allen-Cahn equation on closed manifolds
• Minimal hypersurfaces of least area
• Min-max for phase transitions and the existence of embedded minimal hypersurfaces
• Weyl law for the volume spectrum
• Convergence of phase interfaces in the van der Waals-Cahn-Hilliard theory.
• The catenoid estimate and its geometric applications
• On the multiplicity one conjecture in min-max theory
• A proof of the multiplicity 1 conjecture for min-max minimal surfaces in arbitrary codimension
• Morse index of multiplicity one min-max minimal hypersurfaces
• Minimal surfaces and the Allen-Cahn equation on 3-manifolds: index, multiplicity, and curvature estimates
• The second inner variation of energy and the Morse index of limit interfaces
• Existence of infinitely many minimal hypersurfaces in positive Ricci curvature
• Min-max theory and the Willmore conjecture
• A general regularity theory for stable codimension 1 integral varifolds
• Stable phase interfaces in the van der Waals–Cahn–Hilliard theory
• Regularity of stable minimal hypersurfaces
• Spectrum and index of two-sided Allen–Cahn minimal hypersurfaces
• The role of minimal surfaces in the study of the Allen-Cahn equation
• Finite Morse Index Implies Finite Ends
• Variational Methods
• Riemannian geometry and geometric analysis

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