We develop a multivalued theory for the stability operator of (a constant multiple of) a minimally immersed submanifold $Sigma$ of a Riemannian manifold $mathcal{M}$. 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 $Sigma$ 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.

Multiple valued Jacobi fields / S. Stuvard. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - 58:3(2019 May 08), pp. 92.1-92.83.

Multiple valued Jacobi fields

S. Stuvard
2019-05-08

Abstract

We develop a multivalued theory for the stability operator of (a constant multiple of) a minimally immersed submanifold $Sigma$ of a Riemannian manifold $mathcal{M}$. 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 $Sigma$ 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.
Almgren's Q-valued functions; Stability operator; Linearization around high multiplicity cones
Settore MAT/05 - Analisi Matematica
Article (author)
File in questo prodotto:
File Dimensione Formato  
Multiple valued Jacobi fields_final.pdf

accesso aperto

Tipologia: Post-print, accepted manuscript ecc. (versione accettata dall'editore)
Dimensione 1.05 MB
Formato Adobe PDF
1.05 MB Adobe PDF Visualizza/Apri
Stuvard2019_Article_MultipleValuedJacobiFields.pdf

accesso riservato

Tipologia: Publisher's version/PDF
Dimensione 1.1 MB
Formato Adobe PDF
1.1 MB Adobe PDF   Visualizza/Apri   Richiedi una copia
Pubblicazioni consigliate

Caricamento pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/850370
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 1
social impact