Chaire Aisenstadt 2008 Aisenstadt Chair
Professor Gerhard Huisken (MaxPlanckInstitut für Gravitationsphysik) 

Une série de conférences / A series of lectures


Geometric Variational Problems in General Relativity The Einstein equations governing gravitational phenomena in General Relativity can be derived from a variational principle for the Lorentzian metric of a curved spacetime. It turns out that as a consequence physical concepts related to gravity such as energy, momentum and center of mass are also best formulated in terms of variational structures on Lorentzian manifolds. The lecture explains the interaction between new methods in analysis and differential geometry and physical concepts in the study of isolated gravitationg systems. Cette conférence s'adresse à un large auditoire.
Le vendredi 18 avril 2008 / Friday, April 18, 2008 16 h / 4:00 pm
Université de Montréal Pavillon AndréAisenstadt, 2920, ch. de la Tour Salle / Room 6214
Une réception suivra la conférence au Salon Mauricel'Abbé, Pavillon AndréAisenstadt (Salle 6245). There will be a reception after the lecture in Salon Mauricel'Abbé, Pavillon AndréAisenstadt (Room 6245). 

Mean Curvature Flow and Isoperimetric Inequalities


The evolution of hypersurfaces in direction of their unit normal with speed given by their mean curvature is a quasilinear parabolic system that decreases area while smoothing the evolving hypersurfaces in a natural way. The lecture explains how weak solutions of mean curvature flow and mean curvature flow with surgeries can be used to prove isoperimetric inequalities. 

Le lundi 21 avril 2008 / Monday, April 21, 2008 10 h / 10:00 am
Université de Montréal, Pavillon AndréAisenstadt 2920, ch. de la Tour Salle / Room 6214 

Inverse Mean Curvature Flow


The evolution of hypersurfaces in direction of the inverse of their mean curvature is more nonlinear in nature than mean curvature flow. While expanding the area of evolving surfaces at an exponential rate this flow improves several natural integral invariants of the surface. These monotonicity results persist even in the presence of jumps in weak solutions of the flow and leads to applications in conformal geometry and General Relativity. 

Le mardi 22 avril 2008 / Tuesday, April 22, 2008 10 h / 10:00 am
Université de Montréal Pavillon AndréAisenstadt, 2920, ch. de la Tour Salle / Room 6214 

An Isoperimetric Concept for the Mass in General Relativity


The total energy of an isolated gravitating system such as a star or a black hole can be described in terms of a geometric invariant of an asymptotically flat 3manifold arsing as a spacelike slice in a Lorentuzian 4manifold. It turns out that this geometric invariant can be characterised in terms of isoperimetric properties of the 3manifold. The proof of its major properties relies on techniques from mean curvature flow and inverse mean curvature flow discussed in the previous lectures. 

Le mercredi 23 avril 2008 / Wednesday, April 23, 2008 11 h / 11:00 am
Université de Montréal Pavillon AndréAisenstadt, 2920, ch. de la Tour Salle / Room 6214 