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- Date de réalisation : 24 Juin 2015
- Durée du programme : 85 min
- Classification Dewey : Mathématiques
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- Catégorie : Cours magistraux
- Niveau : niveau Doctorat (LMD), Recherche
- Disciplines : Géométrie
- Collections : Ecoles d'été, 2015
- ficheLom : Voir la fiche LOM
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- Réalisateur(s) : Bastien Fanny
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- Langue : Anglais
- Mots-clés : mathématiques, Grenoble, école d'été, institut fourier, summer school, geometric measure theory, calculus of variation
- Conditions d’utilisation / Copyright : CC BY-NC-ND 4.0
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Camillo De Lellis - Center manifolds and regularity of area-minimizing currents (Part 3)
A celebrated theorem of Almgren shows that every integer rectifiable current which minimizes (locally) the area is a smooth submanifold except for a singular set of codimension at most 2. Almgren’s theorem is sharp in codimension higher than 1, because holomorphic subvarieties of Cn are area-minimizing. In fact the typical singularity of a 2-dimensional area-minimizing current is modelled by branch points of holomorphic curves. These singularities are rather difficult to analyze because they might be very high order phenomena.
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