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Date
Editeur
Auteur
Titre
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Joseph Fu - Integral geometric regularity (Part 3)
/ Fanny Bastien
/ 24-06-2015
/ Canal-u.fr
Fu Joseph
Voir le résumé
Voir le résumé
In the original form given by Blaschke
in the 1930s, the famous Principal Kinematic Formula expresses the Euler
characteristic of the intersection of two sufficiently regular objects
in euclidean space, integrated over the space of all possible relative
positions, in terms of geometric invariants associated to each of them
individually. It is natural to wonder about the precise regularity
needed for this to work. The question turns on the existence of the
normal cycle of such an object A, i.e. an integral current that stands
in for its manifolds of unit normals if A is too irregular for the
latter to exist in a literal sense. Despite significant recent progress,
a comprehensive understanding of this construction remains maddeningly
elusive. In these lectures we will discuss both of these aspects. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, geometric measure theory, calculus of variation
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Accéder à la ressource
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Joseph Fu - Integral geometric regularity (Part 2)
/ Fanny Bastien
/ 23-06-2015
/ Canal-u.fr
Fu Joseph
Voir le résumé
Voir le résumé
In the original form given by Blaschke
in the 1930s, the famous Principal Kinematic Formula expresses the Euler
characteristic of the intersection of two sufficiently regular objects
in euclidean space, integrated over the space of all possible relative
positions, in terms of geometric invariants associated to each of them
individually. It is natural to wonder about the precise regularity
needed for this to work. The question turns on the existence of the
normal cycle of such an object A, i.e. an integral current that stands
in for its manifolds of unit normals if A is too irregular for the
latter to exist in a literal sense. Despite significant recent progress,
a comprehensive understanding of this construction remains maddeningly
elusive. In these lectures we will discuss both of these aspects. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, geometric measure theory, calculus of variation
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Accéder à la ressource
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Joseph Fu - Integral geometric regularity (Part 1)
/ Fanny Bastien
/ 22-06-2015
/ Canal-u.fr
Fu Joseph
Voir le résumé
Voir le résumé
In the original form given by Blaschke
in the 1930s, the famous Principal Kinematic Formula expresses the Euler
characteristic of the intersection of two sufficiently regular objects
in euclidean space, integrated over the space of all possible relative
positions, in terms of geometric invariants associated to each of them
individually. It is natural to wonder about the precise regularity
needed for this to work. The question turns on the existence of the
normal cycle of such an object A, i.e. an integral current that stands
in for its manifolds of unit normals if A is too irregular for the
latter to exist in a literal sense. Despite significant recent progress,
a comprehensive understanding of this construction remains maddeningly
elusive. In these lectures we will discuss both of these aspects. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, geometric measure theory, calculus of variation
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Accéder à la ressource
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Camillo De Lellis - Center manifolds and regularity of area-minimizing currents (Part 5)
/ Fanny Bastien
/ 25-06-2015
/ Canal-u.fr
De Lellis Camillo
Voir le résumé
Voir le résumé
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. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, geometric measure theory, calculus of variation
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Camillo De Lellis - Center manifolds and regularity of area-minimizing currents (Part 2)
/ Fanny Bastien
/ 23-06-2015
/ Canal-u.fr
De Lellis Camillo
Voir le résumé
Voir le résumé
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. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, geometric measure theory, calculus of variation
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Accéder à la ressource
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Guy David - Minimal sets (Part 3)
/ Fanny Bastien
/ 24-06-2015
/ Canal-u.fr
David Guy
Voir le résumé
Voir le résumé
indisponible Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, geometric measure theory, calculus of variation
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Accéder à la ressource
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Guy David - Minimal sets (Part 1)
/ Fanny Bastien
/ 23-06-2015
/ Canal-u.fr
David Guy
Voir le résumé
Voir le résumé
indisponible Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, geometric measure theory, calculus of variation, minimal sets
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Andrea Braides - Geometric measure theory issues from discrete energies
/ Fanny Bastien
/ 29-06-2015
/ Canal-u.fr
Braides Andrea
Voir le résumé
Voir le résumé
indisponible Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, geometric measure theory, calculus of variation
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Giovanni Alberti - Introduction to minimal surfaces and finite perimeter sets (Part 4)
/ Giovanni Alberti
/ 18-06-2015
/ Canal-u.fr
Bastien Fanny
Voir le résumé
Voir le résumé
In these lectures I will first
recall the basic notions and results that are needed to study minimal
surfaces in the smooth setting (above all the area formula and the first
variation of the area), give a short review of the main (classical)
techniques for existence results, and then outline the theory of Finite
Perimeter Sets, including the
main results of the theory (compactness, structure of distributional
derivative, rectifiability). If time allows, I will conclude with a few
applications. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, geometric measure theory, calculus of variation
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Nicholas Alikakos - On the structure of phase transition maps : density estimates and applications
/ Fanny Bastien
/ 02-07-2015
/ Canal-u.fr
Alikakos Nicholas
Voir le résumé
Voir le résumé
indisponible Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, geometric measure theory, calculus of variation
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Accéder à la ressource
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