Uniqueness of Kähler-Ricci solitons

By G. Tian, Xiaohua Zhu. 2000

167 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/18e9b9c3a7621f739a073f9ebac5bf54eb0f7a98

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In Applied Mathematics

In Astronomy and Astrophysics

In Geometry and Topology

Citations in the corpus

Frankel conjecture and Sasaki geometry (2012, background): “We also state some facts about SasakiRicci solitons, whose proofs follow analogously the Kähler case as in [60, 61].”
Kahler geometry on toric manifolds, and some other manifolds with large symmetry (2008, methodology): “Then if K is the set where v ≤ 1 we have Vol(K) ≤ Cλ−1/2 for some constant C depending only on the dimension n. Wang and Zhu prove this using a comparison argument.”
Tian's properness conjectures and Finsler geometry of the space of Kahler metrics (2015, unknown): “The following lemma is well-known [70, 63].”
Kähler–Einstein metrics along the smooth continuity method (2015, methodology): “(11) Ric(ωφ)− Lvωφ = tωφ + (1− t)ωψ, which is the natural continuity path for finding Kähler-Ricci solitons, used by TianZhu [48] for instance.”
A Brunn–Minkowski type inequality for Fano manifolds and some uniqueness theorems in Kähler geometry (2013, background): “(Tian-Zhu,[30], [31]) LetX be a Fano manifold and let ω0 andω1 be solutions of 10.”
Hamiltonian 2-forms in Kähler geometry, IV weakly Bochner-flat Kähler manifolds (2005, background): “In particular, a number of uniqueness results for such metrics have been established [16, 17], as well as existence results in the case of toric Fano manifolds [18] and certain geometrically ruled complex manifolds [10].”
Kähler metrics with constant weighted scalar curvature and weighted K‐stability (2018, unknown): “[12, 16, 82, 83]) fits in to our setting too.”
Complex optimal transport and the pluripotential theory of K\"ahler-Ricci solitons (2014, result): “Our next result extends the Tian-Zhu uniqueness theorem for Kähler-Ricci solitons [47, 48] (which in turn generalizes the Bando-Mabuchi uniqueness theorem for Kähler-Einstein metrics) to the singular setting.”