Extremal metrics on toric surfaces: a continuity method

118 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

The complex Monge–Ampère equation on compact Kähler manifolds (2010, background): “Recently, Donaldson solved the constant scalar curvature equation on toric Kähler surfaces with K-stability in a series of paper [23, 25, 26, 27, 28].”
The greatest Ricci lower bound, conical Einstein metrics and Chern number inequality (2012, methodology): “For each n-dimensional integral Delzant polytope P , as in [12, 13], we consider the set of pairs {p, vp,i}, where p is a vertex of P and the neighboring faces are given by lp,i(x) = vp,i ·x−λp,i > 0 for i = 1, .”
On the constant scalar curvature Kähler metrics, general automorphism group (2018, background): “However, if one examines carefully the original papers of Donaldson [27], [28], [29] on this subject, it is already known through work there that L1 stability implies both filtrated stability and uniform stability, from which properness of K-energy follows.”
Kahler geometry on toric manifolds, and some other manifolds with large symmetry (2008, background): “f) vanishes if fis aﬃne linear and LA(f) >0 if fis a convex function which is not aﬃne linear, then there is an admissible symplectic potential satisfying the equation uij ij= −A. We refer to [9], [10], [11] for more information about this, particularly in the case when n= 2. 19 3 Toric Fano mani”