A nonlinear inequality of Moser-Trudinger type

By G. Tian, Xiaohua Zhu. 2000

61 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/f929a21cc463a92838d5fe17d90b8ea7f69476e2

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Some discretizations of geometric evolution equations and the Ricci iteration on the space of Kähler metrics (2007, background): “(ii) [T5,T6, TZ1 ] Assume that Aut(M, J) is finite.6 Then the properness of F1 (or”
Geometric pluripotential theory on Kähler manifolds (2019, background): “Numerous conjectures were proposed during this time, a number of which where adressed in the case of Fano manifolds without vectorfields [63, 104, 109].”
The Kähler–Ricci flow with positive bisectional curvature (2007, methodology): “Chen-Tian [CT] used the Moser-Trudinger inequalities [T1, TZ1 ] (see also [PSSW1]) to show that if there exists a K¨ahler-Einstein metric then, starting at a metric with positive bisectional curvature, the flow converges to it. Perelman later showed, without any curvature conditions, that the flow ”
On the convergence and singularities of the J‐Flow with applications to the Mabuchi energy (2004, background): “For the precise definition, see section 2. This result is already known [Ti3, Ti4, TiZh ] when c1(M) is a multiple of [χ0].”
The Moser-Trudinger inequality on Kähler-Einstein manifolds (2006, background): “• It was shown by Tian-Zhu [24] that the assumption (1.8) can be removed so that (1.3) holds with the γ of Step 1.”
The greatest Ricci lower bound, conical Einstein metrics and Chern number inequality (2012, background): “It is first proved in [44, 47] for the properness of F -functional on Fano Kähler-Einstein manifolds without holomorphic vector fields.”
Adams' inequalities for bi-Laplacian and extremal functions in dimension four (2009, unknown): “We should also mention that Tian and Zhu [40] proved a Moser–Trudinger type inequality for almost plurisubharmonic functions on any Kahler–Einstein manifolds with positive scalar curvature which generalizes the stronger version of the Moser–Onofri inequality on S 2 and also refines a weaker inequali”
Tian's properness conjectures and Finsler geometry of the space of Kahler metrics (2015, background): “(85) Tian–Zhu proved the following result [63, Appendix A].”
Kähler–Ricci solitons on compact complex manifolds with C1(M) > 0 (2005, unknown): “Inequality (0.2) generalizes the corresponding one in [T] and [ TZ1 ].”