ICTP Geometic Analysis Seminar 2016 - TOMORROW Thursday 3 March at 14:00

[Math Section]

G E O M E T R I C   A N A L Y S I S   S E M I N A R S   2016


Thursday, 3 March, at 14:00 hrs.




Niels Martin Møller (ICTP)


"Prescribing (constant) scalar curvature"

Abstract:
In this on-going scalar curvature seminar series, we last time heard 
from Claudio Arezzo about the role of scalar curvature in the theory of 
Sacks-Uhlenbeck/Schoen-Yau concerning existence of harmonic maps and 
incompressible minimal surfaces. The main conclusion was of the form: 
For a Riemannian 3-manifold (M^3, g), having positive scalar curvature 
implies a topological phenomenon: That there are no 'holes' inside M^3 
which 'look like' a genus >=1 surface.

This time around we will look at a different (but related) aspect,using 
the theory of Kazdan-Warner and Yamabe/Trudinger/Aubin/Schoen: Given a 
manifold M^n, which functions (and of special interest: the constant 
ones) can be the scalar curvature of some metric on M^n?".
The setting here is to start with a metric g and search only within the 
same conformal class [g], which is a natural reduction of the problem to 
"just" one second order nonlinear PDE in one scalar function on M.




VENUE: SISSA, room 133