A new holomorphic invariant and uniqueness of Kähler-Ricci solitons

By G. Tian, Xiaohua Zhu. 2002

201 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/14a35007b71786d4bc49a46f0eb203706db9533e

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. Robert J. Berman
2. Chi Li
3. Song Sun
4. Xiuxiong Chen
5. G'abor Sz'ekelyhidi
6. B. Berndtsson
7. Jiyuan Han
8. S. Boucksom

In Astronomy and Astrophysics

1. Song Sun
2. Robert J. Berman
3. Chi Li
4. Abdellah Lahdili
5. B. Berndtsson
6. Jiyuan Han
7. Weiyong He
8. Xiuxiong Chen

In Geometry and Topology

1. Robert J. Berman
2. Chi Li
3. Song Sun
4. Xiuxiong Chen
5. G'abor Sz'ekelyhidi
6. S. Boucksom
7. B. Berndtsson
8. Mattias Jonsson

Citations in the corpus

• Transverse Kähler geometry of Sasaki manifolds and toric Sasaki-Einstein manifolds (2006, methodology): “This is a Sasakian version of a result of Wang and Zhu [41] in the Kählerian case.”
• Rotationally symmetric shrinking and ex - panding gradient Kahler - Ricci solitons (2003, unknown): “A soliton on a compact K¨ ahler manifold is unique modulo the identity component of the holomorphic automorphism group [41, 42, 44 ], generalizing the classic result for K¨ ahler-Einstein metrics [5].”
• On the Yau‐Tian‐Donaldson Conjecture for Generalized Kähler‐Ricci Soliton Equations (2020, methodology): “) This is a generalization of the Mabuchi functional defined in [78], but different from the one used in [13] and [45] (See Remark 9.”
• Complex optimal transport and the pluripotential theory of K\"ahler-Ricci solitons (2014, methodology): “Tian-Zhu’s modified functionals and Futaki invariant.”
• Calabi flow, Geodesic rays, and uniqueness of constant scalar curvature K\ (2010, methodology): “When the manifold is Fano, the uniqueness of Kähler-Einstein metrics was previously proved by Bando-Mabuchi [2], and it was later gener- alized to the case of Kähler-Ricci solitons by Tian-Zhu [49].”
• ASYMPTOTIC CHOW SEMI-STABILITY AND INTEGRAL INVARIANTS (2004, methodology): “When M is a Fano manifold Tian and Zhu [17] used it to show the uniqueness of Kähler–Ricci solitons.”
• Kähler metrics with constant weighted scalar curvature and weighted K‐stability (2018, background): “Thus, the theory of gradient Kähler–Ricci solitons (see, for example, [12, 17, 86, 87]) fits in to our setting too.”