On degenerate Monge-Ampère equations over closed Kähler manifolds

By Zhou Zhang. 2006

91 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/c0b9cc273bf4c6a84a1770aadcd34b8340058d8c

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

On stability and continuity of bounded solutions of degenerate complex Monge–Ampère equations over compact Kähler manifolds (2010, background): “The proof of (2) appears in [18], Section 4 (p.”
The complex Monge–Ampère equation on compact Kähler manifolds (2010, background): “3) when F̃ is less regular and/or when ω is degenerate, to mention [55, 8, 33, 21, 29, 22] to name a few.”
Metrics with cone singularities along normal crossing divisors and holomorphic tensor fields (2011, background): “Kołodziej [24] (see also [16], [36], [31], [6], [33], [34] for substantial improvements and interesting applications of this result):”
The Kähler–Ricci flow on Hirzebruch surfaces (2009, methodology): “Hence, we can apply the results of [16], [41], [8] on the complex Monge–Ampère equation to obtain an Ly bound on j which is uniform in t.”
Continuity of Extremal Transitions and Flops for Calabi-Yau Manifolds (2010, background): “In [18] (see also [66]), a generalized Calabi–Yau theorem was obtained, which says that if M0 is a Calabi–Yau variety, then for any ample line bundle L0 there is a unique Ricci-flat Kähler form ω ∈ c1(L0).”
Contracting exceptional divisors by the Kähler–Ricci flow II (2010, background): “2]) if follows from it follows from [7, 11, 34] that φT and hence ψT is continuous.”
The greatest Ricci lower bound, conical Einstein metrics and Chern number inequality (2012, background): “By standard argument from [16, 55], ω converges as ǫ → 0 to the unique Kähler-Einstein metric gcan on the canonical model Xcan of X in C ∞ local topology away from the exceptional locus the pluricanonical system.”
Geometric estimates for complex Monge–Ampère equations (2017, background): “The following proposition generalizes the result in [4, 10, 15, 42] by studying a family of collapsing complex Monge–Ampère equations.”
The Kähler–Ricci flow through singularities (2009, background): “In this section, we review some of the important results in degenerate complex Monge–Ampère equations developed by Kolodziej [20] and many others ([10, 13,14,50]).”