The Moser-Trudinger inequality on Kähler-Einstein manifolds

By Duong H. Phong, Jian Song, Jacob Sturm, B. Weinkove. 2006

88 citations recorded by the source corpus.

We prove the conjecture of Tian on the strong form of the Moser-Trudinger inequality for K\"ahler-Einstein manifolds with positive first Chern class, when there are no holomorphic vector fields, and, more generally, when the setting is invariant under a maximal compact subgroup of the automorphism group.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/5040baab1b9aaedcc27fe5e2932b39d8e261bc66

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Geometric pluripotential theory on Kähler manifolds (2019, background): “The sharpest form of the energy properness condition was identified in [88] and was later adopted in the literature, including in the present work.”
The greatest Ricci lower bound, conical Einstein metrics and Chern number inequality (2012, background): “The J-properness for F is conjectured in this case in [44] and is later proved in [33].”
Tian's properness conjectures and Finsler geometry of the space of Kahler metrics (2015, background): “To cite a few papers from a rapidly growing literature, we mention [16, 43, 52, 19, 53, 46, 69, 68] and references therein.”
Greatest lower bounds on the Ricci curvature of Fano manifolds (2009, methodology): “The statement of the theorem for t = 1 (the second statement replaced with Ric(ω) = ω) follows from the works of Tian [29] and Phong-Song-Sturm-Weinkove [18].”
Extremal metrics and K-stability (PhD thesis) (2006, methodology): “This has been shown in the case of Kähler-Einstein metrics by Tian [33] (see also [27]).”
A thermodynamical formalism for Monge–Ampère equations, Moser–Trudinger inequalities and Kähler–Einstein metrics (2010, background): “As conjectured by Tian and subsequently established in [70] the previous argument can be refined to give that βGβ is even coercive.”