Canonical Metrics In Kahler Geometry

By R. Dresner. 2016

113 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/7643a1a6ec80f39ed7dbbbf434ada7f55ef8ed5a

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Citations in the corpus

Tian's properness conjectures and Finsler geometry of the space of Kahler metrics (2015, unknown): “Recall that for u ∈ E1 ∩ L∞ [59, 4] AM(u) = (I − J)(u) + V −1 ∫”
Regularity of weak minimizers of the K-energy and applications to properness and K-stability (2016, background): “2],[Ti3] and this was proved for Fano manifolds with G trivial [Ti2, TZ].”
Convexity of the K-energy on the space of Kahler metrics and uniqueness of extremal metrics (2014, background): “Chen went on to show [19] that the Mabuchi functional admits an explicit formula which is well-deﬁned along a weak geodesic ray ut as above. (This formula was also independently obtained by Tian, see [52].) Indeed, (1.4) M(u) = E(u)+ ˆ X log( ωn u ωn 0 )ωn u, where the ﬁrst term E(u) is an explicit ”
Smooth and singular Kahler-Einstein metrics (2014, methodology): “Then, a standard Moser iteration argument [246] gives a uniform control on the C norm of φ(s) in terms of I(ω, ωφ(s)), which is in turn controlled under the properness assumption.”
G-uniform stability and Kähler–Einstein metrics on Fano varieties (2019, background): “These functionals first appeared in Kähler geometry in the smooth setting (see [74]).”
Comparison and vanishing theorems for Kähler manifolds (2018, background): “Here 〈·, ·〉 is the bilinear extension of the Riemannian product and the curvatureR follows the convention of [31].”
Optimal destabilizing centers and equivariant K-stability (2020, methodology): “As another application, we recover the K-stability of Fermat hypersurfaces, as well as smooth complete intersections of two quadrics [2,38].”
Geometric pluripotential theory on Kähler manifolds (2019, background): “Motivated by results in conformal geometry, the relationship between energy properness and existence of canonical metrics in Kähler geometry goes back to the work of Tian and collaborators in the nineties [103, 105].”
Existence and deformations of Kähler–Einstein metrics on smoothable $\mathbb{Q}$-Fano varieties (2014, methodology): “First recall that the oscillation of a Kähler potential is controlled by the I functional together with the Poincaré and Sobolev constants bound, see [43].”
Geodesic rays and stability in the cscK problem (2020, methodology): “Following [67], for any > 0 by Jensen’s inequality we get the inequality: ∫”