Degenerate complex Monge-Amp\`ere equations over compact K\"ahler manifolds

By J. Demailly, Nefton Pali. 2007

94 citations recorded by the source corpus.

We prove the existence and uniqueness of the solutions of some very general type of degenerate complex Monge-Amp\`ere equations. This type of equations is precisely what is needed in order to construct K\"ahler-Einstein metrics over irreducible singular K\"ahler spaces with ample or trivial canonical sheaf and singular K\"ahler-Einstein metrics over varieties of general type.

View Paper: https://www.semanticscholar.org/paper/28b37d54a7fe2f1ed1ff49566d5e236fc8f920bb

Citations in the corpus

• Fully non-linear parabolic equations on compact Hermitian manifolds (2017, unknown): “We refer to [26, 11, 8, 23, 24, 41, 58, 59, 30, 31] and references therein.”
• Canonical measures and Kähler-Ricci flow (2008, background): “Recently, Demailly and Pali proved the following uniform estimate and we refer the readers to the general statement in [ DePa ].”
• Adiabatic limits of Ricci-flat Kähler metrics (2009, methodology): “bound on ϕt was conjectured. When m= 1 such a bound can be easily proved using the Moser iteration method (see [ST1]). The bound in the general case was then proved independently by Demailly and Pali [DP] and by Eyssidieux, Guedj and Zeriahi [EGZ2]: Theorem 2.1 ([DP, EGZ2]). There is a constant Ctha”