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Ricci entropy, RCD structures and Kahler spaces
Bin Guo, Jian Song, Jacob Sturm
This paper is the final installment in our series on the geometric theory of complex Monge-Ampere equations. We study singular Kahler metrics on compact normal Kahler spaces with k…
Geometric Holder estimates for complex Monge-Ampere equations
Bin Guo, Jian Song, Jacob Sturm
This paper is the continuation of our earlier work on Holder estimates for Kahler potentials on compact normal Kahler spaces. We establish a geometric counterpart for analytic Hold…
Geometric stability for complex Monge-Ampere equations
Bin Guo, Jian Song, Jacob Sturm
Let be a compact Kahler manifold. The analytic stability theorem of Kolodziej for complex Monge-Ampere equation states that for any Kahler metrics and in the same coho…
Diameter estimates in Kähler geometry II: removing the small degeneracy assumption
Bin Guo, Duong H. Phong, Jian Song +1
In this short note, we remove the small degeneracy assumption in our earlier works [10, 11]. This is achieved by a technical improvement of Corollary 5.1 in [10]. As a consequence,…
Sobolev inequalities on Kähler spaces
Bin Guo, Duong H. Phong, Jian Song +1
We establish a uniform Sobolev inequality for Kähler metrics, which only require an entropy bound and no lower bound on the Ricci curvature. We further extend our Sobolev inequalit…