The second inner variation of energy and the Morse index of limit interfaces

DOI10.1007/s12220-018-00134-7zbMath1443.53022arXiv1710.04719OpenAlexW2964117006MaRDI QIDQ2303783

Pedro Gaspar

Publication date: 5 March 2020

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1710.04719

zbMATH Keywords

phase transitionsminimal surfacesAllen-Cahn equation

Mathematics Subject Classification ID

Minimal surfaces and optimization (49Q05) Nonlinear elliptic equations (35J60) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items

Classification of finite Morse index solutions to the elliptic sine-Gordon equation in the plane, 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, Nondegeneracy and stability in the limit of a one-phase singular perturbation problem, An improved Morse index bound of min-max minimal hypersurfaces, Mean curvature flow and low energy solutions of the parabolic Allen-Cahn equation on the three-sphere, The p-widths of a surface, Multiplicity‐1 minmax minimal hypersurfaces in manifolds with positive Ricci curvature, Symmetric mean curvature flow on the \(n\)-sphere, Spectrum and index of two-sided Allen–Cahn minimal hypersurfaces, Regularity of minimal and CMC stable hypersurfaces: a brief overview, 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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