Comptes Rendus
no. 5
Partial Differential Equations
Partial regularity for homogeneous complex Monge–Ampere equations
[Régularité partielle pour des équations de Monge–Ampère complexes]

Présenté par : Jean-Michel Bismut

Xiuxiong Chen1 ; Gang Tian1
1 Department of Mathematics, University of Wisconsin, Madison, WI 53706-1, USA
Comptes Rendus. Mathématique, Volume 340 (2005) no. 5, pp. 337-340.

Dans cette Note, on établit un nouveau résultat de égularité partielle pour certaines équations complexes de Monge–Ampère. On obtient ces résultats en étudiant des feuilletages par des disques holomorphes et leurs relations avec ces équations.

In this Note, we establish a new partial regularity theory on certain homogeneous complex Monge–Ampere equations. This partial regularity theory is obtained by studying foliations by holomorphic disks and their relation to these equations.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2004.11.024
Xiuxiong Chen 1 ; Gang Tian 1

1 Department of Mathematics, University of Wisconsin, Madison, WI 53706-1, USA 
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Xiuxiong Chen; Gang Tian. Partial regularity for homogeneous complex Monge–Ampere equations. Comptes Rendus. Mathématique, Volume 340 (2005) no. 5, pp. 337-340. doi : 10.1016/j.crma.2004.11.024. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.11.024/

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[3] X.X. Chen; G. Tian Uniqueness of extremal Kähler metrics, C. R. Acad. Sci. Paris, Ser. I, Volume 340 (2005) no. 4

[4] X.X. Chen, G. Tian, Geometry of Kähler metrics and foliations by holomorphic discs, Preprint, 2004

[5] S.K. Donaldson Holomorphic discs and the complex Monge–Ampere equation, J. Symplectic Geometry, Volume 1 (2002), pp. 171-196

[6] Y.-G. Oh Riemann–Hilbert problem and application to the perturbation theory of analytic discs, Kyungpook Math. J., Volume 35 (1995), pp. 38-75

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