Supremum of Perelman's entropy and Kähler-Ricci flow on a Fano manifold
By G. Tian, Shijin Zhang, Zhenlei Zhang, Xiaohua Zhu. 2011
56 citations recorded by the source corpus.
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].
Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/cc97871de9903627128660ec7ee09c25f4cd5471
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In Applied Mathematics
- G'abor Sz'ekelyhidi
- R. Dervan
- Chi Li
- Zhenlei Zhang
- G. Tian
- S. Boucksom
- Mattias Jonsson
- Robert J. Berman
In Astronomy and Astrophysics
- G'abor Sz'ekelyhidi
- R. Dervan
- Zhenlei Zhang
- G. Tian
- Song Sun
- Jian Song
- Robert J. Berman
- Yanir A. Rubinstein
In Geometry and Topology
- G'abor Sz'ekelyhidi
- R. Dervan
- Chi Li
- Zhenlei Zhang
- G. Tian
- S. Boucksom
- Mattias Jonsson
- Robert J. Berman
Citations in the corpus
- The Kähler–Ricci flow and optimal degenerations (2016, methodology): “Finally, using a result of Tian-Zhang-Zhang-Zhu [36], we obtain a general convergence result for the Kähler-Ricci flow, assuming the existence of a Kähler-Ricci soliton.”
- Regularity of Kähler–Ricci flows on Fano manifolds (2013, methodology): “In view of the main result in [43], one should be able to prove that under the assumption of Theorem 1.”