18 citations · 31 across the 10 of their papers we have counts for
9 papers · 1 filter
One Dimensional Asymptotic Plateau Problem in -Dimensional Asymptotically Conical Manifolds
Jiayin Liu, Shijin Zhang, Yuan Zhou
Let be an asymptotically conical Riemannian manifold having dimension , opening angle and pos…
A gap theorem on complete shrinking gradient Ricci solitons
Shijin Zhang
In this short note, using Günther's volume comparison theorem and Yokota's gap theorem on complete shrinking gradient Ricci solitons, we prove that for any complete shrinking gradi…
Gradient Kähler-Ricci solitons with nonnegative orthogonal bisectional curvature
Shijin Zhang
In this paper, we prove that any complete shrinking gradient Kähler-Ricci solitons with positive orthogonal bisectional curvature must be compact. We also obtain a classification o…
Remarks on shrinking gradient Kähler-Ricci solitons with positive bisectional curvature
Guoqiang Wu, Shijin Zhang
In this short note, using an argument by Munteanu and Wang, we provide an alternative proof of the fact first obtained by Lei Ni that shrinking gradient Kähler-Ricci solitons with…
Liouville-type theorems on the complete gradient shrinking Ricci solitons
Huabin Ge, Shijin Zhang
We prove that there does not exist non-constant positive -harmonic function on the complete gradient shrinking Ricci solitons. We also prove the $L^{p}(p\geq 1 \ {\rm or}\ 0<p\l…
The Kähler-Ricci flow on Fano bundles
Xin Fu, Shijin Zhang
We study the behavior of the Kähler-Ricci flow on some Fano bundle which is a trivial bundle on one Zariski open set. We show that if the fiber is blown up at one…
Remarks on symplectic mean curvature flows in Kähler surfaces with positive holomorphic sectional curvatures
Shijin Zhang
In this paper, we mainly study the mean curvature flow in Kähler surfaces with positive holomorphic sectional curvatures. First, we prove that if the ratio of the maximum and t…
3-Dimensional Discrete curvature flows and discrete Einstein metric
Huabin Ge, Xu Xu, Shijin Zhang
We introduce the discrete Einstein metrics as critical points of discrete energy on triangulated 3-manifolds, and study them by discrete curvature flow of second (fourth) order. We…
Supremum of Perelman's entropy and Kähler-Ricci flow on a Fano manifold
Gang Tian, Shijin Zhang, Zhenlei Zhang +1
In this paper, we extend the method in [TZhu5] to study the energy level of Perelman's entropy for Kähler-Ricci flow on a Fano manifold. Consequently, we firs…