There has been fundamental progress in complex differential geometry in the last two decades. For one, The uniformization theory of canonical Kähler metrics ha

The Yau-Tian-Donaldson conjecture for anti-canonical polarization was recently solved affirmatively by Chen-Donaldson-Sun and Tian. However, this conjecture is

A basic problem in differential geometry is to find canonical metrics on manifolds. The best known example of this is the classical uniformization theorem for R

Kähler geometry is a beautiful and intriguing area of mathematics, of substantial research interest to both mathematicians and physicists. This self-contained

This edited volume has a two-fold purpose. First, comprehensive survey articles provide a way for beginners to ease into the corresponding sub-fields. These are