A comparison of the Almgren-Pitts and the Allen-Cahn min-max theory

DOI10.1007/s00039-022-00610-xOpenAlexW3015229685MaRDI QIDQ2088126

Akashdeep Dey

Publication date: 21 October 2022

Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.05120

zbMATH Keywords

Allen-Cahn widthsAlmgren-Pitts min-max theory

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Variational problems in a geometric measure-theoretic setting (49Q20) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91)

Related Items (6)

An improved Morse index bound of min-max minimal hypersurfaces ⋮ Multiplicity of solutions to the multiphasic Allen-Cahn-Hilliard system with a small volume constraint on closed parallelizable manifolds ⋮ The first width of non-negatively curved surfaces with convex boundary ⋮ Double-well phase transitions are more rigid than minimal hypersurfaces ⋮ The p-widths of a surface ⋮ Convergence of the self‐dual U(1)‐Yang–Mills–Higgs energies to the (n−2)$(n-2)$‐area functional

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