On stability and the convergence of the Kähler-Ricci flow

By Duong H. Phong, Jacob Sturm. 2006

135 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/da1982bdedb68836ccb12db878151f12dbff3a18

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In Applied Mathematics

In Astronomy and Astrophysics

In Geometry and Topology

Citations in the corpus

Contracting exceptional divisors by the Kähler–Ricci flow II (2010, background): “Convergence is also known under certain weaker assumptions (see [6, 14, 17, 18, 27, 31, 37] and the discussions therein).”
The Kähler–Ricci flow on Hirzebruch surfaces (2009, background): “ity conditions to prove convergence properties of the Kähler–Ricci flow is an area of considerable current interest and we refer the reader to [21], [19], [22], [23], [25], [31], [24], [36] and [5] for some recent advances (however, this list of references is far from complete).”
Infinite time singularities of the Kähler-Ricci flow (2014, background): “In fact, it is easy to see that this convergence is exponentially fast; see [17].”
The Chern–Ricci flow on complex surfaces (2012, background): “1 implies convergence, one can follow the arguments of Phong-Sturm [39].”
The Kähler–Ricci flow with positive bisectional curvature (2007, methodology): “Now we recall from [ PS3 ] that for a solution g(t) of the K¨ahler-Ricci flow, the function Y (t) = R X |∇u| 2 ! n satisfies”
Lectures on Stability and Constant Scalar Curvature (2008, methodology): “Condition (B) is the following condition [111]: (B): There exists no almost-complex structure J̃ in the C closure of the orbitDiff(X)· J with dimH(X, T 1,0 J̃ ) > dimH(X, T 1,0 J ) (6.”
Multiplier Ideal Sheaves and the K\"ahler-Ricci Flow (2006, background): “We already know that ∂j∂k̄φ̇ = −(Rk̄j − gk̄j) → 0 in all Sobolev norms if the curvature is bounded and the Mabuchi energy is bounded from below ([21], Theorem 1).”
Space of Ricci Flows I (2009, background): “For other important progress in Kähler Ricci flow, we refer interested readers to the following papers(far away from being complete): [72], [110], [109], [101], [111], [79], [101], [78], [68], [104], [88], as well as references listed therein.”
The Kähler–Ricci flow through singularities (2009, background): “We refer the readers to an incomplete list of literatures [24,25,27,28,37,43,44] for some recent development.”
Existence of approximate Hermitian-Einstein structures on semi-stable bundles (2010, methodology): “[21, 22]), which is a more non-linear analogue of the gradient flow of the Donaldson functional.”
The Kähler-Ricci flow and K-polystability (2008, background): “Combined with the result of Phong-Song-Sturm-Weinkove [16] we obtain exponential convergence.”