arXiv subjects
Publications and source records attributed to Zhu-Hong Zhang.
We establish three circles theorems for subharmonic functions on Riemannian manifolds with nonnegative Ricci curvature, as well as on gradient shrinking Ricci solitons with scalar curvature bounded from below by $\frac{n-2}{2}$. We also establish a three circiles theorem for holomorphic functions on gradient shrinking Kähler-Ricci solitons with some curvature conditions. As applications, we prove some Liouville type theorems.
A gradient Ricci soliton is a triple $(M,g,f)$ satisfying $R_{ij}+\nabla_i\nabla_j f=λg_{ij}$ for some real number $λ$. In this paper, we will show that the completeness of the metric $g$ implies that of the vector field $\nabla f$.
In this paper, we will give a local version of the Hamilton-Ivey type pinching estimate of the gradient shrinking soliton with vanishing Weyl tensor, and then give a complete classification on gradient shrinking solitons with vanishing Weyl tensor.
In this paper, we will give an extension of Mok's theorem on the generalized Frankel conjecture under the condition of the orthogonal bisectional curvature.