The Monge-Ampère equation on compact Kähler manifolds

By S. Kołodziej. 2003

149 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/acb51f8928cc72ee7420c34c1ced845428bdd742

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. G'abor Sz'ekelyhidi
2. B. Weinkove
3. Valentino Tosatti
4. Xiuxiong Chen
5. Duong H. Phong
6. Robert J. Berman
7. Song Sun
8. Simon Donaldson

In Geometry and Topology

1. G'abor Sz'ekelyhidi
2. B. Weinkove
3. Valentino Tosatti
4. Xiuxiong Chen
5. Duong H. Phong
6. Robert J. Berman
7. Song Sun
8. Jian Song

In Statistical and Nonlinear Physics

1. Xiuxiong Chen
2. S. Dinew
3. B. Weinkove
4. Valentino Tosatti
5. Song Sun
6. Simon Donaldson
7. V. V. Hung
8. Nguyen Van Phu

Citations in the corpus

• A Priori L∞-Estimates for Degenerate Complex Monge–Ampère Equations (2010, unknown): “The purpose of this note is to (re)prove this result without any technical assumption and with a different method: we actually follow the strategy introduced by Kołodziej in [9, 10] and further developed in [3, 6].”
• The arithmetic Hodge index theorem for adelic line bundles (2013, unknown): “We refer to Calabi [6] for the original theorem and to Kolodziej [23] and Błocki [3] for some regularity extensions.”
• A priori estimates for complex Hessian equations (2011, methodology): “As in [Kołodziej 2003] one can show that capm(K ) is comparable with cap ′ m(K ): There exists C > 0 such that 1 C capm(K )≤ cap ′ m(K )≤ C capm(K ).”
• Multiplier Ideal Sheaves and the K\"ahler-Ricci Flow (2006, unknown): “R IC C I FLO W 1 D.H.Phong ,Natasa Sesum ,and Jacob Sturm y A bstract M ultiplieridealsheavesareconstructed asobstructionsto theconvergenceofthe K ahler-Ricci ow on Fano m anifolds,following earlier constructions ofK ohn,Siu, and Nadel,and using therecentestim atesofK olodziejand Perelm an.”
• The Chern–Ricci flow on complex surfaces (2012, methodology): “We do not expect that there is any fundamental obstacle to establishing (iv) and (v) under the condition (∗), since the methods used (estimates obtained via the maximum principle, the weak solution constructed by Song-Tian [44], the results of Ko lodziej [28]) can most likely be generalized to this ”
• Kahler-Einstein metrics on Fano manifolds, I: approximation of metrics with cone singularities (2012, methodology): “Then, either following the uniqueness in [15] or Proposition 2.”
• Hessian measures on m-polar sets and applications to the complex Hessian equations (2017, background): “The aimof the present paper is to study the convergence inCm, C̃m-capacity andHessian measures onm-polar set which is a generalization of results in [14] and[15].”