Concavity of Perelman's $\mathcal{W}$-functional over the space of K\'ahler potentials

Autor: Pali, Nefton
Rok vydání: 2016
Předmět:
Zdroj: European Journal of Mathematics, 3 (2017), no. 3, 587-602
Druh dokumentu: Working Paper
Popis: In this short note we observe that the concavity of Perelman's $\mathcal{W}$-functional over a neighborhood of a K\"ahler-Ricci soliton inside the space of K\"ahler potentials is a direct consequence of author's solution of the variational stability problem for K\"ahler-Ricci solitons. Independently, we provide a rather simple proof of this fact based on some elementary formulas obtained in our previous work.
Databáze: arXiv