Concavity of Perelman's -functional over the space of Kähler potentials
arXiv:1605.09290
Abstract
In this short note we observe that the concavity of Perelman's -functional over a neighborhood of a Kähler-Ricci soliton inside the space of Kähler potentials is a direct consequence of author's solution of the variational stability problem for Kähler-Ricci solitons. Independently, we provide a rather simple proof of this fact based on some elementary formulas obtained in our previous work.