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

Abstract

In this paper, we extend the method in [TZhu5] to study the energy level $L(\cdot )$ of Perelman's entropy $\lambda (\cdot )$ for Kähler-Ricci flow on a Fano manifold. Consequently, we first compute the supremum of $\lambda (\cdot )$ in Kähler 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 Kähler-Ricci flow in [TZhu3].

28 pages

References in corpus (1)

• Convergence of Kähler-Ricci flow on Fano manifolds, II

Cited by in corpus (2)

• Ricci flow and birational surgery
• Regularity of Kähler-Ricci flow