On the Kähler-Ricci Flow on Projective Manifolds of General Type

By G. Tian, Zhou Zhang. 2006

269 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/8a4a93f9accd989ba33b27708614770817a60eda

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

On the evolution of a Hermitian metric by its Chern-Ricci form (2011, methodology): “In the special case when ω0 is Kähler, this is already known by the result of Tian-Zhang [51], who extended earlier work of Cao and Tsuji [8, 56, 57].”
The Kähler–Ricci flow on surfaces of positive Kodaira dimension (2006, unknown): “[ClKoMo]). Such X is called a minimal model of general type and the Kahler–Ricci flow deforms any Kahler metric to a unique singular Kahler–Einstein metric on X (see [Ts, TiZha ]).”
Infinite time singularities of the Kähler-Ricci flow (2014, background): “In the first setup (which is the same as in Tosatti [24], Gross, Tosatti and Published: 20 October 2015 DOI: 10.2140/gt.2015.19.2925 Zhang [8; 9], Hein and Tosatti [11] and Tosatti, Weinkove and Yang [27]) we let .”
Kähler currents and null loci (2013, background): “See also [26,31,46–48,52–54,64] for more results about finite time singularities of the Kähler–Ricci flow.”
A Priori L∞-Estimates for Degenerate Complex Monge–Ampère Equations (2010, unknown): “Then, it is known [4, 14] that the expanding Kähler–Ricci flow { d dt ω(t , ·) = −Ricω(t , ·) − ω(t , ·) ω(0, ·) = ω0 ( ) at U nieristÃ © Paul Saatier on M ay (1)7, 2016 htp://im rn.”
The Kähler–Ricci flow through singularities (2009, methodology): “It is later improved by Dinew and Zhang [11] (also see [10] for more general cases) for big and semi-ample classes.”
The Kähler–Ricci flow on Hirzebruch surfaces (2009, methodology): “This result is essentially contained in [34], [41], but we will include an outline of the proof for the reader’s convenience.”
On the structure of almost einstein manifolds (2012, unknown): “[40]), the Ricci flow ∂ ∂t g = −Ric+λig has a solution with g(0) = gi on Mi × [0, 1] so long as λi[ωi] + ( ei − 1 ) c1(Mi) > 0, where ωi denotes the Kähler form of gi.”
The Chern–Ricci flow on complex surfaces (2012, methodology): “Given what we have proved, the following result can now be established using the arguments of [55] for the Kähler-Ricci flow: Lemma 2.”
The Monge–Ampère equation for non-integrable almost complex structures (2016, methodology): “Again, using the techniques developed in this paper one should be able to characterize the maximal existence time of this flow, exactly as in [42, 49].”
On the Kahler Ricci flow on projective manifolds of general type (2015, background): “2) has long time existence [27], and we will show that solutions to (4.”