Supremum of Perelman's entropy and Kähler-Ricci flow on a Fano manifold

Details Supremum of Perelman's entropy and Kähler-Ricci flow on a Fano manifold Supremum of Perelman's entropy and Kähler-Ricci flow on a Fano manifold

2011-07-20

arxiv.org/abs/1107.4018v1

Mathematics

Differential Geometry

28 pages

Scientific paper

In this paper, we extend the method in [TZhu5] to study the energy level $L(\cdot)$ of Perelman's entropy $\lambda(\cdot)$ for K\"ahler-Ricci flow on a Fano manifold. Consequently, we first compute the supremum of $\lambda(\cdot)$ in K\"ahler class $2\pi c_1(M)$ under an assumption that the modified Mabuchi's K-energy $\mu(\cdot)$ defined in [TZhu2] is bounded from below. Secondly, we give an alternative proof to the main theorem about the convergence of K\"ahler-Ricci flow in [TZhu3].

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