Pédagogie > geometric measure theory
http://indexation.univ-fcomte.fr/ori-oai-search/
Thu, 28 May 2020 20:27:13 GMTGiovanni Alberti - Introduction to minimal surfaces and finite perimeter sets (Part 1)Sun, 14 Jun 2015 22:00:00 GMTIn
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.
http://indexation.univ-fcomte.fr/ori-oai-search/notice/view/oai%253Acanal-u.fr%253A22067
oai:canal-u.fr:22067URL: http://indexation.univ-fcomte.fr/ori-oai-search/notice/view/oai%253Acanal-u.fr%253A22067 ]]>Giovanni Alberti - Introduction to minimal surfaces and finite perimeter sets (Part 5)Wed, 17 Jun 2015 22:00:00 GMTIn 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.
http://indexation.univ-fcomte.fr/ori-oai-search/notice/view/oai%253Acanal-u.fr%253A22129
oai:canal-u.fr:22129URL: http://indexation.univ-fcomte.fr/ori-oai-search/notice/view/oai%253Acanal-u.fr%253A22129 ]]>Nicholas Alikakos - On the structure of phase transition maps : density estimates and applicationsWed, 01 Jul 2015 22:00:00 GMTindisponible
http://indexation.univ-fcomte.fr/ori-oai-search/notice/view/oai%253Acanal-u.fr%253A22133
oai:canal-u.fr:22133URL: http://indexation.univ-fcomte.fr/ori-oai-search/notice/view/oai%253Acanal-u.fr%253A22133 ]]>Giovanni Alberti - Introduction to minimal surfaces and finite perimeter sets (Part 4)Wed, 17 Jun 2015 22:00:00 GMTIn 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.
http://indexation.univ-fcomte.fr/ori-oai-search/notice/view/oai%253Acanal-u.fr%253A22121
oai:canal-u.fr:22121URL: http://indexation.univ-fcomte.fr/ori-oai-search/notice/view/oai%253Acanal-u.fr%253A22121 ]]>Andrea Braides - Geometric measure theory issues from discrete energiesSun, 28 Jun 2015 22:00:00 GMTindisponible
http://indexation.univ-fcomte.fr/ori-oai-search/notice/view/oai%253Acanal-u.fr%253A22105
oai:canal-u.fr:22105URL: http://indexation.univ-fcomte.fr/ori-oai-search/notice/view/oai%253Acanal-u.fr%253A22105 ]]>Guy David - Minimal sets (Part 1)Mon, 22 Jun 2015 22:00:00 GMTindisponible
http://indexation.univ-fcomte.fr/ori-oai-search/notice/view/oai%253Acanal-u.fr%253A22139
oai:canal-u.fr:22139URL: http://indexation.univ-fcomte.fr/ori-oai-search/notice/view/oai%253Acanal-u.fr%253A22139 ]]>Guy David - Minimal sets (Part 3)Tue, 23 Jun 2015 22:00:00 GMTindisponible
http://indexation.univ-fcomte.fr/ori-oai-search/notice/view/oai%253Acanal-u.fr%253A22141
oai:canal-u.fr:22141URL: http://indexation.univ-fcomte.fr/ori-oai-search/notice/view/oai%253Acanal-u.fr%253A22141 ]]>Camillo De Lellis - Center manifolds and regularity of area-minimizing currents (Part 2)Mon, 22 Jun 2015 22:00:00 GMTA 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.
http://indexation.univ-fcomte.fr/ori-oai-search/notice/view/oai%253Acanal-u.fr%253A22253
oai:canal-u.fr:22253URL: http://indexation.univ-fcomte.fr/ori-oai-search/notice/view/oai%253Acanal-u.fr%253A22253 ]]>Camillo De Lellis - Center manifolds and regularity of area-minimizing currents (Part 5)Wed, 24 Jun 2015 22:00:00 GMTA 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.
http://indexation.univ-fcomte.fr/ori-oai-search/notice/view/oai%253Acanal-u.fr%253A22155
oai:canal-u.fr:22155URL: http://indexation.univ-fcomte.fr/ori-oai-search/notice/view/oai%253Acanal-u.fr%253A22155 ]]>Joseph Fu - Integral geometric regularity (Part 1)Sun, 21 Jun 2015 22:00:00 GMTIn 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.
http://indexation.univ-fcomte.fr/ori-oai-search/notice/view/oai%253Acanal-u.fr%253A22175
oai:canal-u.fr:22175URL: http://indexation.univ-fcomte.fr/ori-oai-search/notice/view/oai%253Acanal-u.fr%253A22175 ]]>