Displaying similar documents to “Monge-Ampère Equations, Geodesics and Geometric Invariant Theory”

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.

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 .

Convergence of Bergman geodesics on CP 1

Jian Song, Steve Zelditch (2007)

Annales de l’institut Fourier

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The space ℋ of Kähler metrics in a fixed Kähler class on a projective Kähler manifold X is an infinite dimensional symmetric space whose geodesics ω t are solutions of a homogeneous complex Monge-Ampère equation in A × X , where A ⊂ ℂ is an annulus. Phong-Sturm have proven that the Monge-Ampère geodesic of Kähler potentials ϕ ( t , z ) of ω t may be approximated in a weak C 0 sense by geodesics ϕ N ( t , z ) of the finite dimensional symmetric space of Bergman metrics of height N . In this article we prove that ϕ N ( t , z ) → ϕ ( t , z ) in C 2 ( [ 0 , 1 ] × X ) in...