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

2017/10/12 by Pedro Dinis Gaspar, Gaspar, Pedro · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1710.04719

openalex publication_date 2017/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article we study the second variation of the energy functional\nassociated to the Allen-Cahn equation on closed manifolds. Extending well known\nanalogies between the gradient theory of phase transitions and the theory of\nminimal hypersurfaces, we prove the upper semicontinuity of the eigenvalues of\nthe stability operator and consequently obtain upper bounds for the Morse index\nof limit interfaces which arise from solutions with bounded energy and index\nwithout assuming any multiplicity or orientability condition on these\nhypersurfaces. This extends some recent results of N. Le and F. Hiesmayr.\n

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• Smoothness and stability in the Alt-Phillips problem

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