scholarly journals The Continuity Method on Minimal Elliptic Kähler Surfaces

2017 ◽  
Vol 2019 (10) ◽  
pp. 3186-3213 ◽  
Author(s):  
Yashan Zhang ◽  
Zhenlei Zhang
Keyword(s):  
Continuity Method ◽  
Kähler Surfaces

scholarly journals On the limit behavior of metrics in the continuity method for the Kähler–Einstein problem on a toric Fano manifold

2012 ◽  
Vol 148 (6) ◽  
pp. 1985-2003 ◽  
Author(s):  
Chi Li
Keyword(s):  
Ricci Curvature ◽  
Lower Bounds ◽  
Limit Behavior ◽  
Fano Manifold ◽  
Fano Manifolds ◽  
Continuity Method ◽  
Type Singularity ◽  
Moment Polytope ◽  
The Moment ◽  
Monge Ampere

AbstractThis work is a continuation of the author’s previous paper [Greatest lower bounds on the Ricci curvature of toric Fano manifolds, Adv. Math. 226 (2011), 4921–4932]. On any toric Fano manifold, we discuss the behavior of the limit metric of a sequence of metrics which are solutions to a continuity family of complex Monge–Ampère equations in the Kähler–Einstein problem. We show that the limit metric satisfies a singular complex Monge–Ampère equation. This gives a conic-type singularity for the limit metric. Information on conic-type singularities can be read off from the geometry of the moment polytope.

scholarly journals A new method of constructing scalar-flat Kähler surfaces

1995 ◽  
Vol 41 (2) ◽  
pp. 449-477 ◽  
Author(s):  
Jongsu Kim ◽  
Massimiliano Pontecorvo
Keyword(s):  
New Method ◽  
Kähler Surfaces

scholarly journals On Hamiltonian stationary Lagrangian spheres in non-Einstein Kähler surfaces

2011 ◽  
Vol 271 (1-2) ◽  
pp. 257-270 ◽  
Author(s):  
Ildefonso Castro ◽  
Francisco Torralbo ◽  
Francisco Urbano
Keyword(s):  
Kähler Surfaces ◽  
Hamiltonian Stationary
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