Uniqueness and stability for the complex Monge-Ampère equation on compact Kähler manifolds

By Zbigniew Blocki. 2003

49 citations recorded by the source corpus.

We prove uniqueness of weak solutions of the Dirichlet problem for the complex Monge-Ampere equation on compact Kahler manifolds. A qualitative version of this result implies the L 2n/(n-1) - L 1 stability of solutions of this equation.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/370f3fb0e2d30780a8e42e56b37952499f541430

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In Applied Mathematics

1. Shou-wu Zhang
2. Zbigniew BÃlocki
3. Xinyi Yuan
4. Askold Khovanskii
5. Kiumars Kaveh

In Geometry and Topology

1. Xinyi Yuan
2. Shou-wu Zhang
3. Zbigniew BÃlocki
4. Wei Zhang
5. C. Skinner
6. Ye Tian
7. P. Michel
8. Gergely Harcos

Citations in the corpus

• The arithmetic Hodge index theorem for adelic line bundles (2013, methodology): “When the base field isC, all of these are essentially due to the original work of Calabi [6] and the later extension by Błocki [3].”
• ON GEODESICS IN THE SPACE OF KÄHLER METRICS (2011, methodology): “To prove the most general result we have to follow a method from [5].”
• Formes différentielles réelles et courants sur les espaces de Berkovich (2012, unknown): “Plus récemment, l’unicité d’une métrique conduisant à une mesure prescrite (théorème de Calabi) est prouvée dans [57] en adaptant la preuve de [12].”
• A Priori L∞-Estimates for Degenerate Complex Monge–Ampère Equations (2010, unknown): “It follows from the seminal work of Yau [16] and Kołodziej [9], that Equation ( )t admits a unique continuous solution (see also [2] for uniqueness).”