Boltzmann’s Entropy and Kahler-Ricci Solitons

We discuss an entropy functional of Boltzmann’s type defined on Kahler metrics in a fixed Kahler class. This functional is monotonically increasing along the Kahler-Ricci flow and has Kahler-Ricci solitons as its critical points. We derive and second variational formula and show that any Kahler-Ricci solitons (including Kahler-Einstein metrics) are linearly stable with respect to this functional. In this talk, the speaker will survey some related results about this functional and explain the significance of this second variation result.