BOUNDING SCALAR CURVATURE AND DIAMETER ALONG THE KÄHLER RICCI FLOW (AFTER PERELMAN)

By N. Šešum, G. Tian. Journal of the Institute of Mathematics of Jussieu, 2008

196 citations recorded by the source corpus.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/aa17f761e9b64c27b02873f1643565031b65a5b6

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Citations in the corpus

The Kähler–Ricci flow and optimal degenerations (2016, methodology): “When ωKRS is actually Kähler-Einstein, this was proven by Tian-Zhu [37, 38] using Perelman’s estimates [27, 34] (see also [13]).”
Multiplier Ideal Sheaves and the K\"ahler-Ricci Flow (2006, methodology): “Sim ilar ideas were exploited by Tian-Zhu [26]in theirproofofan inequality ofHarnack typefortheK ahler-Ricci ow.”
Frankel conjecture and Sasaki geometry (2012, methodology): “He also proved very deep results for the Kähler-Ricci flow on Fano manifolds, namely, that the scalar curvature and the diameter are uniformly bounded along the flow; details of his results can be found in [52].”
A Lie algebraic approach to Ricci flow invariant curvature conditions and Harnack inequalities (2010, background): “By an argument of Perelman which was written up by Sesum and Tian [2006] (M,λig(ti)) subconverges to a compact limit manifold (M, g∞).”
Regularity of Kähler–Ricci flows on Fano manifolds (2013, background): “2) Also by Perelman, the diameter and scalar curvature of g(t) are uniformly bounded (see [38] for a proof).”
The Kähler–Ricci flow on Hirzebruch surfaces (2009, background): “This situation has been wellstudied and the convergence result of (b)(i) is an immediate consequence of the diameter bound of Perelman for the normalized Kähler–Ricci flow [18], [26].”
Contracting exceptional divisors by the Kähler–Ricci flow II (2010, background): “It was shown in [16, 19, 30] that on a manifold with positive first Chern class the flow converges to a Kähler– Einstein metric when one exists.”