Canonical Metrics in Kahler Geometry

By G. Tian. 2000

124 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/fa435c4447bf35584a70204cae84e3215732e113

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Hyperdiscriminant polytopes, Chow polytopes, and Mabuchi energy asymptotics (2008, unknown): “1(t)( _’ tg 1(t) @ @z ’_ t jTj2 z jTj2 + @ @z ’ t ) + jTj2 z jTj2 + @ @z ’ t )g11(t) @ @z ’_ t= ’_ t: (6.35) Therefore, D(K) = Z Z ( 1) _’ t( 2! ’t + Ric(! ’t )) : As is well known (see [45] pg. 58 ) we have that 2 Z Z (6.36) ’_ t! ’t = 2dF !(’ ˙) : By deﬁnition of the Mabuchi energy (see (3.1))”
Kähler–Einstein metrics and the Kähler–Ricci flow on log Fano varieties (2011, methodology): “t step in this direction was taken in [BBGZ09], which combined a variational approach with the ﬁnite energy formalism of [GZ07, BEGZ10] to give a new perspective on the classical results of Ding-Tian [Tian]. These techniques were then extended by the ﬁrst named author in [Ber10], where an adequate e”
Existence and non-existence of solutions for a class of Monge–Ampère equations (2009, unknown): “[10] and references therein.”
Real Monge-Ampere equations and Kahler-Ricci solitons on toric log Fano varieties (2012, unknown): “e, by deﬁnition, that E(MA(φ)) = E(φ,φ0) − ˆ X (φ−φ0)MA(φ) It should be pointed out that in the case when Xis smooth the corresponding formula 4.1 is equivalent to a previous formula of Tian and Chen [54]. We next come back to the setting of convex functions in Rnassociated to a convex body P,taking”
On uniform estimate in Calabi-Yau theorem (2005, background): “[5], p. 91 and ref. [ 6 ], p. 49). Copyright by Science in China Press 2005 On uniform estimate in Calabi-Yau theorem 245”
A gradient estimate in the Calabi–Yau theorem (2009, unknown): “[15] or [6]): if φ satisfies (0.”