Mathematics Seminar at ICTP - NEXT WEEK

[Math]

M A T H E M A T I C S  S E M I N A R S  2007


Tuesday, 20 February, at 14:00 hrs.


Dr. Cheikh Birahim Ndiaye
(SISSA)


"Constant Q-curvature conformal metrics in arbitrary dimension"

Abstract:  In this talk, we will discuss the problem of finding metrics
with constant Q-curvature on a given closed Riemannian manifold (M,g)  
with
dimension an arbitrary integer n>3. This will be equivalent to  
solving an
n-th order elliptic PDE ( if n is even) or an n-th order elliptic  
integral
equation (if n is odd ) with exponential nonlinearity  and  variational
structure in both cases. However when the total integral of the
Q-curvature is large, the Euler-Lagrange functional associated is
unbounded from below,
implying that we have to find critical points of saddle point type.  
Using
a min-max scheme whose construction is based on concentration of volume,
we solve the problem under general assumptions which are also  
conformally
invariant.


Venue: Seminar room (ICTP Main Building, first floor)