Stability of extremal Kahler manifolds

By T. Mabuchi. 2004

67 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/186271e88b0b219a87a12012647a0917b43a66e6

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

In Geometry and Topology

Citations in the corpus

Extremal metrics on blowups (2006, methodology): “Condition (i) and (ii) should be related to Mabuchi’s T -stability [21] and to Szekelyhidi’s relative K-stability [29] in the same way the analogue conditions for constant scalar curvature metrics are related to the asymptotic Chow semi-stability along the line of ideas described by Thomas in [30] (”
Scalar curvature and projective embeddings, II (2004, background): “hy paper, discussing various extensions and ramiﬁ- cations of the ideas sudied in [6]. However this plan has been modiﬁed in the light of subsequent developments. On the one hand, Mabuchi [11], [12], [13] has extended the results of [6] to the case where the varieties have inﬁnitesimal automorphims.”
Extremal metrics and K‐stability (2004, background): “The maximal torus contains a distinguished C∗-action χ, generated by the extremal vector field (see Futaki and Mabuchi [6]).”
An energy-theoretic approach to the Hitchin-Kobayashi correspondence for manifolds, I (2004, methodology): “Then by [14], Theorem B, there exist Fk 2 tR, real numbers k 2 R, and smooth real-valued K -invariant functions 'k , k = 1, 2, : : : , on M such that, for each ` 2 Z 0, we have (3.”
Calabi flow and projective embeddings (2008, background): “The restriction on Aut(X,L) in Donaldson’s Theorem 3 has been relaxed by Mabuchi [22, 23], whilst the picture in [13] has been related to the Deligne pairing by Phong–Sturm in [25, 26], an approach which also leads to a sharpening of some estimates.”
K-stability of constant scalar curvature polarization (2008, background): “Let ψ : C∗ → SL(N,C) be an algebraic group homomorphism chosen in such a way that the induced action of t ∈ C∗, |t| ≤ 1, on ∆ × PN−1(C) defined by ∆ × PN(C) ∋ (z, p) 7→ (tz, ψ(t) · p) ∈ ∆ × PN−1(C) maps X into X .”
CM Stability and the Generalized Futaki Invariant I (2006, background): “For example, the reader is invited to consu lt , as a rather small sample, the following papers [9, 8, 5, 28, 29, 1, 21, 22, 15].”
Positivity of direct image bundles and convexity on the space of Kähler metrics. (2006, result): “This certainly does not give the results in [7], [1],[13] and [6], as the existence of smooth geodesics is an open and ev e dubious issue, (see [5] and [6] for the best results in this direction ), but at least it indicates a seemingly interesting relation between our res ults on flatness of direct ”
K-stability of constant scalar curvature Kähler manifolds (2008, unknown): “[10].”
The complex Monge–Ampère equation on compact Kähler manifolds (2010, background): “Thorough the efforts of many mathematicians, the necessary part of this conjecture is essentially done ([50, 23, 26, 17, 41, 47, 48] ).”