The partial $C^0$-estimate along the continuity method
By G'abor Sz'ekelyhidi. 2013
62 citations recorded by the source corpus.
We prove that the partial $C^0$-estimate holds for metrics along Aubin's continuity method for finding Kahler-Einstein metrics, confirming a special case of a conjecture due to Tian. We use the method developed in recent work of Chen-Donaldson-Sun on the analogous problem for conical Kahler-Einstein metrics.
View Paper: https://www.semanticscholar.org/paper/0b23f72709bb3043d3307593194d6199e5af5a4d
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Citations in the corpus
- A variational approach to the Yau–Tian–Donaldson conjecture (2015, methodology): “Shortly thereafter, a proof based on the ‘classical’ continuity method was provided by Datar and Sz´ekelyhidi [Sz´e16,DS16], followed by another one by Chen–Sun–Wang [CSW18], based on the K¨ahler–Ricci flow.”
- K-polystability of Q-Fano varieties admitting Kähler-Einstein metrics (2012, methodology): “One motivation for using Aubin’s original method here is that Tian’s conjecture on the partial C−estimate (see H1 below) has now been proved along Aubin’s continuity method when X is smooth (see [65] which builds on[16]) and one can thus hope that it will eventually also be established on singular F”
- On the Yau‐Tian‐Donaldson Conjecture for Generalized Kähler‐Ricci Soliton Equations (2020, result): “When X and Θ are smooth, it might be possible to generalize the metric techniques (including Cheeger-Colding-Tian theory and partial C-estimates) in [84, 51, 75, 28, 80, 64, 72] to prove similar results, although F.”