101 citations · 386 across the 36 of their papers we have counts for
33 papers · 1 filter
Diameter estimates in Kähler geometry
Bin Guo, Duong H. Phong, Jian Song +1
Diameter estimates for Kähler metrics are established which require only an entropy bound and no lower bound on the Ricci curvature. The proof builds on recent PDE techniques for $…
Moment map, convex function and extremal point
King Leung Lee, Jacob Sturm, Xiaowei Wang
The moment map is a central concept in the study of Hamiltonian actions of compact Lie groups on symplectic manifolds. In this short note, we propose a theory of moment map…
Green's functions and complex Monge-Ampère equations
Bin Guo, Duong H. Phong, Jacob Sturm
Uniform and lower bounds are obtained for the Green's function on compact Kähler manifolds. Unlike in the classic theorem of Cheng-Li for Riemannian manifolds, the lower boun…
An Analytic Proof of the Stable Reduction Theorem
Jian Song, Jacob Sturm, Xiaowei Wang
The stable reduction theorem says that a family of curves of genus over a punctured curve can be uniquely completed (after possible base change) by inserting certain stab…
Continuity of the Weil-Petersson potential
Jian Song, Jacob Sturm, Xiaowei Wang
Let (resp. ) be the the moduli space of -dimensional Kähler-Einstein manifolds (resp. varieties) with ample. We prove t…
Riemannian geometry of Kahler-Einstein currents III: compactness of Kahler-Einstein manifolds of negative scalar curvature
Jian Song, Jacob Sturm, Xiaowei Wang
Let be the set of -dimensional compact Kahler-Einstein manifolds satisfying with volume bounded above by . We prove that after pass…