Biqiang Zhao

activity

20222026

collaborators

10 papers

math.AP2026

Nonexistence of solutions to $Δ_{p} u + Δ_{q} u + u^{s} ∣\nabla u ∣^{t} \leq 0$ on geodesically complete noncompact Riemannian manifolds

Biqiang Zhao

In this paper, we consider the inequality $Δ_{p} u + Δ_{q} u + u^{s} ∣\nabla u ∣^{t} \leq 0$ on geodesically complete noncompact Riemannian manifolds. By a test function argument, we establish Liou…

math.AP2026

On nonnegative solutions of the parabolic differential inequality with $(p, q)$ -Laplace on Riemannian manifolds

Biqiang Zhao

In this paper, we establish Liouville-type theorems for parabolic differential inequalities with $(p, q) -$ Laplacian operator on Riemannian manifolds. By a test function argument, we…

math.AP2026

On nonnegative solutions of the differential inequality $Δ_{p} u + Δ_{q} u + V (x) u^{s} \leq 0$ on Riemannian manifolds

Biqiang Zhao

In this paper, we are concerned with differential inequalities with $(p, q)$ -Laplacian operator on Riemannian manifolds. Using a test function argument, we establish Liouville-type…

math.DG2025

A Liouville theorem for the CR Yamabe type equation on Sasakian manifolds

Biqiang Zhao

In this paper, we study the CR Yamabe type equation \begin{align} Δ_b u+F(u)=0 \nonumber \end{align} on complete noncompact $(2 n + 1)$ -dimensional Sasakian manifolds with nonnegative…

math.AP2025

Liouville theorem for the inequality $Δ_{m} u + f (u) \leq 0$ on Riemannian manifolds

Biqiang Zhao

In this paper, we study the quasilinear inequality $Δ_{m} u + f (u) \leq 0$ on a complete Riemannian manifold, where \begin{align*} m>1,α>m-1 \quad and \quad f(t)> 0,αf(t)-tf^{'}(t)\geq…

math.AP2025

Liouville type results for semilinear elliptic equation and inequality on Sasakian manifolds

Biqiang Zhao

In this paper, we study the semilinear elliptic equation and inequality on Sasakian manifolds. First, we obtain Liouville theorems for the equation $Δ_{b} u + F (u) = 0$ based on a genera…

math.DG2025

On $\partial_{b}$ -harmonic maps from pseudo-Hermitian manifolds to Kähler manifolds

Yuxin Dong, Hui Liu, Biqiang Zhao

In this paper, we consider maps from pseudo-Hermitian manifolds to Kähler manifolds and introduce partial energy functionals for these maps. First, we obtain a foliated Lichnerowic…

math.DG2024

Gradient estimates for $Δ_{b} u + a u^{p + 1} = 0$ on pseudo-Hermitian manifolds

Biqiang Zhao

In this paper, we derive the gradient estimates for the positive solutions of the equation $Δ_{b} u + a u^{p + 1} = 0$ on complete noncompact pseudo-Hermitian manifolds, where $a > 0$ a…

math.DG2023

Gradient Estimates For The CR Heat Equation On Complete noncompact Pseudo-Hermitian Manifolds

Yuxin Dong, Yibin Ren, Biqiang Zhao

In this paper, we derive local and global Li-Yau type gradient estimates for the positive solutions of the CR heat equation on complete noncompact pseudo-Hermitian manifolds. As ap…

math.DG2022

The Existence of Pseudoharmonic Maps For Small Horizontal Energy

BiQiang Zhao

In this paper, we consider the pseudoharmonic heat flow with small initial horizontal energy and give the existence of pseudoharmonic maps from closed pseudo-Hermitian manifolds to…

Nonexistence of solutions to Δp​u+Δq​u+us∣∇u∣t≤0 on geodesically complete noncompact Riemannian manifolds

On nonnegative solutions of the parabolic differential inequality with (p,q)-Laplace on Riemannian manifolds

On nonnegative solutions of the differential inequality Δp​u+Δq​u+V(x)us≤0 on Riemannian manifolds

A Liouville theorem for the CR Yamabe type equation on Sasakian manifolds

Liouville theorem for the inequality Δm​u+f(u)≤0 on Riemannian manifolds

Liouville type results for semilinear elliptic equation and inequality on Sasakian manifolds

On ∂b​-harmonic maps from pseudo-Hermitian manifolds to Kähler manifolds

Gradient estimates for Δb​u+aup+1=0 on pseudo-Hermitian manifolds

Gradient Estimates For The CR Heat Equation On Complete noncompact Pseudo-Hermitian Manifolds

The Existence of Pseudoharmonic Maps For Small Horizontal Energy

Nonexistence of solutions to $Δ_{p} u + Δ_{q} u + u^{s} ∣\nabla u ∣^{t} \leq 0$ on geodesically complete noncompact Riemannian manifolds

On nonnegative solutions of the parabolic differential inequality with $(p, q)$ -Laplace on Riemannian manifolds

On nonnegative solutions of the differential inequality $Δ_{p} u + Δ_{q} u + V (x) u^{s} \leq 0$ on Riemannian manifolds

Liouville theorem for the inequality $Δ_{m} u + f (u) \leq 0$ on Riemannian manifolds

On $\partial_{b}$ -harmonic maps from pseudo-Hermitian manifolds to Kähler manifolds

Gradient estimates for $Δ_{b} u + a u^{p + 1} = 0$ on pseudo-Hermitian manifolds