A new eigenvalue problem for free boundary minimal submanifolds in the\n unit ball

2019/01/06 by Baptiste Devyver, Devyver, Baptiste · 1 citation
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1901.01530

openalex publication_date 2019/01/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The purpose of the present paper is to show that the components of the unit\nnormal of any minimal surface with free boundary in the unit ball, are\neigenfunctions associated with the eigenvalue -2, for some (new) natural\neigenvalue problem for the Jacobi operator; this fact has analytic (spectral)\nconsequences for free boundary minimal surfaces in the unit 3-ball of index\n4, and might prove useful in order to characterize these. This is also in\nstrong analogy with the case of minimal surfaces in S³.\n

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