2017/01/31 by Salvatore Stuvard
Mathematics · #Codimension #Constant (computer programming) #Geometric Analysis and Curvature Flows #Jacobi operator #Manifold (fluid mechanics) #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #Riemannian manifold #Sobolev space #Space (punctuation) #Submanifold #Superposition principle #Vector field #math.AP #math.DG #msc:35J57 #msc:49Q20 #msc:53A10 #msc:54E40
paper · pdf · doi:10.1007/s00526-019-1545-9
published as Calc. Var. Partial Differential Equations 58 (2019), no. 3, Art. 92, 83 pp · 82 pages, 1 figure. Section 9 is new with respect to the previous version
openalex created_date 2017/05/26 · arxiv created 2017/09/25 · openalex publication_date 2019/05/08 · arxiv updated 2019/07/01 · openalex updated_date 2026/08/06
We develop a multivalued theory for the stability operator of (a constant multiple of) a minimally immersed submanifold Σ of a Riemannian manifold M. We define the multiple valued counterpart of the classical Jacobi fields as the minimizers of the second variation functional defined on a Sobolev space of multiple valued sections of the normal bundle of Σ in M, and we study existence and regularity of such minimizers. Finally, we prove that any Q-valued Jacobi field can be written as the superposition of Q classical Jacobi fields everywhere except for a relatively closed singular set having codimension at least two in the domain.