Hölder continuity of solutions to the Monge-Ampère equations on compact Kähler manifolds

Pham Hoang Hiep

Displaying similar documents to “Hölder continuity of solutions to the Monge-Ampère equations on compact Kähler manifolds”

An example of an asymptotically Chow unstable manifold with constant scalar curvature

Hajime Ono, Yuji Sano, Naoto Yotsutani (2012)

Annales de l’institut Fourier

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Donaldson proved that if a polarized manifold $(V, L)$ has constant scalar curvature Kähler metrics in $c_{1} (L)$ and its automorphism group $Aut (V, L)$ is discrete, $(V, L)$ is asymptotically Chow stable. In this paper, we shall show an example which implies that the above result does not hold in the case where $Aut (V, L)$ is not discrete.

Convergence in Capacity

Yang Xing (2008)

Annales de l’institut Fourier

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We study the relationship between convergence in capacities of plurisubharmonic functions and the convergence of the corresponding complex Monge-Ampère measures. We find one type of convergence of complex Monge-Ampère measures which is essentially equivalent to convergence in the capacity $C_{n}$ of functions. We also prove that weak convergence of complex Monge-Ampère measures is equivalent to convergence in the capacity $C_{n - 1}$ of functions in some case. As applications we give certain stability...

On Solvable Generalized Calabi-Yau Manifolds

Paolo de Bartolomeis, Adriano Tomassini (2006)

Annales de l’institut Fourier

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We give an example of a compact 6-dimensional non-Kähler symplectic manifold $(M, κ)$ that satisfies the Hard Lefschetz Condition. Moreover, it is showed that $(M, κ)$ is a special generalized Calabi-Yau manifold.

Monge-Ampère Equations, Geodesics and Geometric Invariant Theory

D.H. Phong, Jacob Sturm (2005)

Journées Équations aux dérivées partielles

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Existence and uniqueness theorems for weak solutions of a complex Monge-Ampère equation are established, extending the Bedford-Taylor pluripotential theory. As a consequence, using the Tian-Yau-Zelditch theorem, it is shown that geodesics in the space of Kähler potentials can be approximated by geodesics in the spaces of Bergman metrics. Motivation from Donaldson’s program on constant scalar curvature metrics and Yau’s strategy of approximating Kähler metrics by Bergman metrics is also...

Compatible complex structures on twistor space

Guillaume Deschamps (2011)

Annales de l’institut Fourier

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Let $M$ be a Riemannian 4-manifold. The associated twistor space is a bundle whose total space $Z$ admits a natural metric. The aim of this article is to study properties of complex structures on $Z$ which are compatible with the fibration and the metric. The results obtained enable us to translate some metric properties on $M$ (scalar flat, scalar-flat Kähler...) in terms of complex properties of its twistor space $Z$ .