Perelman's W-functional and stability of K\"ahler-Ricci flow

Gang Tian; Xiaohua Zhu

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arXiv · 0801.3504

Perelman's W-functional and stability of K\"ahler-Ricci flow

Gang Tian·Xiaohua Zhu

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Abstract

In this expository note, we study the second variation of Perelman's entropy on the space of Kahler metrics at a K\"ahler-Ricci soliton. We prove that the entropy is stable in the sense of variations. In particular, Perelman's entropy is stable along the K\"ahler-Ricci flow. The Chinese version of this note has appeared in a volume in honor of professor K.C.Chang (Scientia Sinica Math., 46 (2016), 685-696).

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Gang Tian, Xiaohua Zhu. 2008-01-23. Perelman's W-functional and stability of K\"ahler-Ricci flow. https://arxiv.org/abs/0801.3504

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