Bo Berndtsson
Variants of the Moser-Trudinger inequality
The classical Moser-Trudinger inequality is an estimate for the integral of the exponential of a function over the Riemann sphere in terms of the $L^2$-norm of its gradient. Generalizations of this to Fano manifolds possessing a Kähler-Einstein metric play an important role in Kähler geometry. We will discuss variants of this for more general complex manifolds and also for domains in $C^n$.
This is joint work with Robert Berman.