We discuss the problem of finding metrics realizing the first conformal eigenvalue. For that purpose we define eigenvalues for certain singular metrics, and discuss volume non-concentration phenomena for maximizing sequences. Eventually we will address the question of regularity properties of an extremal metric.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/3050