Multiplier Ideal Sheaves and the K\"ahler-Ricci Flow

By Duong H. Phong, N. Šešum, Jacob Sturm. 2006

140 citations recorded by the source corpus.

Multiplier ideal sheaves are constructed as obstructions to the convergence of the K\"ahler-Ricci flow on Fano manifolds, following earlier constructions of Kohn, Siu, and Nadel, and using the recent estimates of Kolodziej and Perelman

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/9fb3bb92380d046c0128c456767d6694bcce8c72

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

The Kähler–Ricci flow through singularities (2009, methodology): “As in [26,48], we set As,w,r = (gs,w,r )pr̄ (gs,w,r )(gs,w,r )mt̄ (gs,w,r )pk̄,m(gs,w,r )r̄ s,t̄ , where the covariant derivatives applied to gs,w,r are calculated with respect to a fixed smooth background Kähler metric ĝ.”
The Dirichlet problem for degenerate complex Monge-Ampere equations (2009, background): “The identity of Yau and Aubin is the following, formulated in terms of the endomorphism hk as in [28], Δ′ log Tr h = 1 Tr h (−R + ΔF + (h)mRpkhj)”
Taming symplectic forms and the Calabi–Yau equation (2007, background): “This is a generalization of the third-order estimate of [18] (see also the recent paper [13] for a succinct proof of the parabolic version of this estimate).”
Regularity results for pluriclosed flow (2010, methodology): “These estimates are inspired by Calabi’s third-order estimate of the potential function for the complex Monge–Ampère equation, and similar estimates for the Kähler Ricci flow were considered in Phong, Sesum and Sturm [23].”
On the Kahler Ricci flow on projective manifolds of general type (2015, background): “By standard Schauder estimate ([15]) for parabolic equations, we have Lemma 4.”
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).”
Interior derivative estimates for the Kähler–Ricci flow (2011, unknown): “Following the notation in [Phong et al. 2007], we introduce the endomorphism hi k = ĝi j̄ g j̄ k and let X be the tensor with components X k il = (∇i h · h )l , so that S = |X |2.”