arXiv subjects
Publications and source records attributed to Zhou Zhang.
In this short paper, we show that Kähler-Ricci flows over closed manifolds would have scalar curvature blown-up for finite time singularity. Certain control of the blowing-up is achieved with some mild assumption.
In this paper, we first apply an integral identity on Ricci solitons to prove that closed locally conformally flat gradient Ricci solitons are of constant sectional curvature. We then generalize this integral identity to complete noncompact gradient shrinking Ricci solitons, under the conditions that the Ricci curvature is bounded from below and the Riemannian curvature tensor has at most exponential growth. As a consequence of this identity, we classify complete locally conformally flat gradient shrinking Ricci solitons with Ricci curvature bounded from below.
We generalize and strenghten Kołodziej's stability theorem. In particular we give sharp stability exponent and treat the case with more singular right hand side of the Monge-Ampère equation.
In this note, a modified Kähler-Ricci flow is introduced and studied. The main point is to show the flexibility of Kähler-Ricci flow and summarize some useful techniques.
In this short note, we use classic computations for Kähler-Ricci flow to achieve scalar curvature bound for minimal manifold of general type.
In this work, we study Monge-Ampere equations over closed Kähler manifolds with degenerated cohomology classes. Classic results and arguments in pluripotential theory are generalized a little bit to be applied to our situation.