UNIQUENESS OF EXTREMAL KÄHLER METRICS FOR AN INTEGRAL KÄHLER CLASS

By T. Mabuchi. 2004

59 citations recorded by the source corpus.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/94dc76677c069a1140b52cd9b4ba5c761586d0f6

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. Frank Pacard
2. C. Arezzo
3. C. LeBrun
4. G'abor Sz'ekelyhidi
5. T. Mabuchi
6. Xiuxiong Chen
7. Abdellah Lahdili
8. Weiyong He

In Astronomy and Astrophysics

1. C. Arezzo
2. Frank Pacard
3. C. LeBrun
4. T. Mabuchi
5. G'abor Sz'ekelyhidi
6. Weiyong He
7. Richard P. Thomas
8. Xiuxiong Chen

In Geometry and Topology

1. Frank Pacard
2. C. Arezzo
3. C. LeBrun
4. G'abor Sz'ekelyhidi
5. T. Mabuchi
6. Xiuxiong Chen
7. Abdellah Lahdili
8. Weiyong He

Citations in the corpus

• Hamiltonian 2-forms in Kähler geometry, III extremal metrics and stability (2005, unknown): “Now by Chen–Tian [10, 11] again (see also [14, 40]), there is an automorphism ψ of Ŝ with gŜ = ψ gŜ 0, since these are CSC Kähler metrics in the same Kähler class.”
• Calabi's diastasis function for Hermitian symmetric spaces (2006, unknown): “[2]), stability of complex line bundle and Kähler–Einstein metrics [16–19] and existence and uniqueness of extremal and constant scalar curvature metrics [5,11,12].”
• Blowing up and desingularizing constant scalar curvature Kähler manifolds (2004, methodology): “We know for example, by Mabuchi’s extension of Donaldson’s work [40], [17], that if an integral class is represented by an extremal Kähler metric, then the underlying algebraic manifold is asymptotically stable in a sense which depends on the structure of the automorphism group which preserves the ”
• On Einstein, Hermitian 4-Manifolds (2010, background): “Theorems A, B and C then follow from the uniqueness, up to isometry, of extremal Kähler metrics in a fixed Kähler class [9, 12, 22].”
• K-stability of constant scalar curvature polarization (2008, background): “Following [11], Section 2, we here study the asymptotic behavior of the weighted balanced metrics for polarized algebraic manifolds (M,L) as m → ∞.”
• An energy-theoretic approach to the Hitchin-Kobayashi correspondence for manifolds, I (2004, background): “For a polarized algebraic manifold (M,L) as above with an extremal Kähler metric in the polarization class, there exists an algebraic torus T in H such that the image Φm(M) in P ∗(Vm) is stable relative to T (cf. Section 2 and [14]) for m ≫ 1.”