Spectrum and index of two-sided Allen–Cahn minimal hypersurfaces

DOI10.1080/03605302.2018.1517790zbMath1462.53057arXiv1704.07738OpenAlexW2963090297MaRDI QIDQ4628909

Fritz Hiesmayr

Publication date: 25 March 2019

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1704.07738

zbMATH Keywords

minimal surfacespectrumsecond variationMorse indexJacobi operatorAllen-Cahn equationmin-max

Mathematics Subject Classification ID

Minimal surfaces and optimization (49Q05) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Optimality conditions for minimax problems (49K35) Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91)

Related Items (14)

On upper semicontinuity of the Allen–Cahn twisted eigenvalues ⋮ Generic existence of multiplicity-1 minmax minimal hypersurfaces via Allen-Cahn ⋮ The Weyl law for the phase transition spectrum and density of limit interfaces ⋮ Mean curvature flow and low energy solutions of the parabolic Allen-Cahn equation on the three-sphere ⋮ 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 ⋮ Morse index of multiplicity one min-max minimal hypersurfaces ⋮ Regularity of minimal and CMC stable hypersurfaces: a brief overview ⋮ The second inner variation of energy and the Morse index of limit interfaces ⋮ Compactness of certain class of singular minimal hypersurfaces ⋮ Asymptotic behavior of Allen-Cahn-type energies and Neumann eigenvalues via inner variations ⋮ A comparison of the Almgren-Pitts and the Allen-Cahn min-max theory ⋮ Variational aspects of phase transitions with prescribed mean curvature

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