7 papers
Liouville theorem for quasi-harmonic sphere
Jiayu Li, Linlin Sun
Let be a compact Riemannian manifold whose universal covering supports a convex function. We prove that it admits no quasi-harmonic sphere. No global growth condition is impose…
A flow approach to the Toda system
Yong Luo, Linlin Sun, Guofang Wang
In this paper we introduce a flow to study the Toda system, which we call {\it Toda flow.} More generally, we introduce a flow of the Liouville systems, formulated as a coupled par…
Critical mean field equations for equilibrium turbulence with sign-changing prescribed functions
Linlin Sun, Xiaobao Zhu
Let be a compact Riemann surface with unit area. We investigate the mean field equation for equilibrium turbulence: \begin{align} \begin{cases} -Δu = ρ_1\left(\frac{h_1e^{u…
Existence results for Toda systems with sign-changing prescribed functions: Part II
Linlin Sun, Xiaobao Zhu
Let be a compact Riemann surface with area . We investigate the Toda system \begin{align} \begin{cases} -Δu_1 = 2ρ_1(h_1e^{u_1}-1) - ρ_2(h_2e^{u_2}-1),\\ -Δu_2 = 2ρ_2(h…
Existence results for Toda systems with sign-changing prescribed functions: Part I
LinLin Sun, Xiaobao Zhu
Let be a compact Riemann surface with area , we shall study the Toda system $$ \begin{cases} -Δu_1 = 2ρ_1(h_1e^{u_1}-1) - ρ_2(h_2e^{u_2}-1),\\ -Δu_2 = 2ρ_2(h_2e^{u_2}-1)…
Sinh-Gordon equations on finite graphs
Linlin Sun
In this paper, we focus on the sinh-Gordon equation on graphs. We introduce a uniform a priori estimate to define the topological degree for this equation with nonzero prescribed f…
Topological degree for Chern-Simons Higgs models on finite graphs
Jiayu Li, Linlin Sun, Yunyan Yang
Let be a finite connected graph. We are concerned about the Chern-Simons Higgs model where is the graph Lapl…