K‐Stability and Kähler‐Einstein Metrics

By G. Tian. 2012

435 citations recorded by the source corpus.

We prove that if a Fano manifold M is K‐stable, then it admits a Kähler‐Einstein metric. It affirms a longstanding conjecture for Fano manifolds. © 2015 Wiley Periodicals, Inc.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/7d72536aeb96968f2984dacbffacf5c1de51f069

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In Applied Mathematics

1. Chi Li
2. Robert J. Berman
3. Mattias Jonsson
4. S. Boucksom
5. Yuchen Liu
6. Tam'as Darvas
7. G. Tian
8. Feng Wang

In Geometry and Topology

1. Chi Li
2. Robert J. Berman
3. Mattias Jonsson
4. S. Boucksom
5. Yuchen Liu
6. G. Tian
7. Feng Wang
8. Tam'as Darvas

Citations in the corpus

• Geodesic rays and stability in the cscK problem (2020, background): “Recently there have been significant progresses towards this conjecture, especially on the analytic part (see [6, 7, 24, 25, 26, 34]) and the Fano case ([27, 69, 30]).”
• A variational approach to the Yau–Tian–Donaldson conjecture (2015, result): “rbitrary polarized varieties, turns out to be equivalent to K-stability in the case of Fano manifolds, in view of [CDS15] and the above result. The main result in [CDS15] (see also [DS15, CSW15], and [Tia15]) is stronger than Theorem A since it allows Xto have nontrivial vector elds. It also uses K-”
• Kähler–Einstein metrics and volume minimization (2016, background): “In particular, the Yau–Tian–Donaldson correspondence has been established for smooth Fano manifolds (see in particular [57], [3], [16,58]).”
• Geometric pluripotential theory on Kähler manifolds (2019, methodology): “Our goal in this chapter is to give equivalent characterizations, more in line with the variational study of partial differential equations, eventually verifying related conjectures of Tian.”
• Conic singularities metrics with prescribed Ricci curvature: the case of general cone angles along normal crossing divisors (2013, result): “ needed in a crucial way so as to bound the holomorphic bisectional curvature of the cone metric outside the aforesaid hypersurface. However, as the spectacular results in [CDS12a, CDS12b, CDS13] and [Tia13] show, it is important to dispose of this kind of results in full generality i.e. without any”