2 citations · 4 across the 5 of their papers we have counts for
5 papers
On some rigidity theorems of Q-curvature
Yiyan Xu, Shihong Zhang
In this paper, we investigate the rigidity of Q-curvature. Specifically, we consider a closed, oriented -dimensional () Riemannian manifold and prove the followi…
MRF-PINN: A Multi-Receptive-Field convolutional physics-informed neural network for solving partial differential equations
Shihong Zhang, Chi Zhang, Bosen Wang
Compared with conventional numerical approaches to solving partial differential equations (PDEs), physics-informed neural networks (PINN) have manifested the capability to save dev…
The moving plane method and the uniqueness of high order elliptic equation with GJMS operator
Shihong Zhang
In this paper, we study the following high order elliptic equation involving the GJMS operator: \begin{align*} αP_{\mathbb{S}^n}v_α+2Q_{g_{\mathbb{S}^n}}=2Q_{g_{\mathbb{S}^n}}e^{nv…
The sharp type Chern-Gauss-Bonnet integral and asymptotic behavior
Shihong Zhang
In this paper, we propose a sharp and quantitative criterion, which focuses solely on curvature, to demonstrate the Chern-Gauss-Bonnet integral. In contrast to the previous res…
A Liouville type theorem of the linearly perturbed Paneitz equation on
Shihong Zhang
We prove a Liouville type theorem for the linearly perturbed Paneitz equation: For small enough, if is a positive smooth solution of $$P_{S^3} u_ε+εu_ε=-u_ε^{-7} \qquad…