scholarly journals Existence of the global solution for the parabolic Monge–Ampère equations on compact Riemannian manifolds

2012 ◽  
Vol 389 (1) ◽  
pp. 597-607 ◽  
Author(s):  
Jianning Huang ◽  
Zhiwen Duan
Keyword(s):  
Global Solution ◽  
Riemannian Manifolds ◽  
Monge Ampere

scholarly journals Monge–Ampère Equations on Riemannian Manifolds

1996 ◽  
Vol 132 (1) ◽  
pp. 126-139 ◽  
Author(s):  
Bo Guan ◽  
YanYan Li
Keyword(s):  
Riemannian Manifolds ◽  
Monge Ampere

scholarly journals The structure of spaces with Bakry–Émery Ricci curvature bounded below

2019 ◽  
Vol 2019 (757) ◽  
pp. 1-50 ◽  
Author(s):  
Feng Wang ◽  
Xiaohua Zhu
Keyword(s):  
Ricci Curvature ◽  
Riemannian Manifolds ◽  
Ricci Solitons ◽  
Existence Problem ◽  
Fano Manifold ◽  
Hausdorff Topology ◽  
Limit Space ◽  
Gromov Hausdorff Topology ◽  
Bounded Below ◽  
Monge Ampere

AbstractWe explore the structure of limit spaces of sequences of Riemannian manifolds with Bakry–Émery Ricci curvature bounded below in the Gromov–Hausdorff topology. By extending the techniques established by Cheeger and Cloding for Riemannian manifolds with Ricci curvature bounded below, we prove that each tangent space at a point of the limit space is a metric cone. We also analyze the singular structure of the limit space as in a paper of Cheeger, Colding and Tian. Our results will be applied to study the limit spaces for a sequence of Kähler metrics arising from solutions of certain complex Monge–Ampère equations for the existence problem of Kähler–Ricci solitons on a Fano manifold via the continuity method.

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