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Supremum of Perelman's entropy and Kahler-Ricci flow on a Fano manifold
Kahler-Ricci flow Kahler-Ricci solitons Perelman entropy
2011/9/15
Abstract: 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 ...
The Kahler-Ricci flow on projective bundles
The Kahler-Ricci flow projective bundles Differential Geometry
2011/9/1
Abstract: We study the behaviour of the K\"ahler-Ricci flow on projective bundles. We show that if the initial metric is in a suitable K\"ahler class, then the fibers collapse in finite time and the m...
Interior derivative estimates for the Kahler-Ricci flow
Interior derivative estimates the Kahler-Ricci flow Differential Geometry
2011/8/31
Abstract: We give a maximum principle proof of interior derivative estimates for the K\"ahler-Ricci flow, assuming local uniform bounds on the metric.