Juncheng Wei

activity

20242026

collaborators

9 papers

math.AP2026

Sharp stability for mixed bubbles on hyperbolic space

Juncheng Wei, Zetian Yan, Zhipeng Yang

We prove sharp residual stability estimates for the critical Poincaré-Sobolev equation near sums of one positive hyperbolic solution and one projected Euclidean bubble in dimension…

math.DG2026

On critical dimensions for compactness in the boundary Yamabe problem, I

Liuwei Gong, Seunghyeok Kim, Monica Musso +1

We construct smooth, non-locally-conformally-flat metrics on the closed ball for which the boundary Yamabe equation admits $L^{\infty}$ -unbounded sequences of positive solutions. The…

math.AP2026

On Brezis' open problem 2.2

Hong-Ge Chen, Yong Liu, Juncheng Wei +1

We prove that the global minimizer of the Ginzburg-Landau energy in the disk of radius $R$ with boundary value $u (x) = \frac{x}{∣ x ∣}$ is the degree-one radial solution of the planar…

math.AP2026

Nonradial stable solutions near the Joseph--Lundgren threshold

Shibing Chen, Yong Liu, Juncheng Wei +1

We study positive stable solutions of the supercritical Lane--Emden equation in the first Joseph--Lundgren interval. For a family of dimensions, we construct nonradial stable entir…

math.AP2026

On Sirakov's equal-frequency uniqueness conjecture

Hong-Ge Chen, Yong Liu, Juncheng Wei +1

Let $N \in {2, 3}$ , $0 < μ_{1} \leq μ_{2}$ , and $0 < β < μ_{1}$ . We prove that the equal-frequency two-component cubic Schrödinger system \[ -Δu+u=μ_1u^3+βuv^2, \qquad -Δv+v=μ_2v^3+βu^2v \quad\te…

math.AP2026

Finite Potential Energy for Entire Solutions of the Planar Ginzburg--Landau Equation

Hongge Chen, Juncheng Wei, Haicheng Yan +1

We prove that every smooth entire solution $u : R^{2} \to R^{2}$ of the Ginzburg--Landau equation $- Δ u = u (1 - ∣ u ∣^{2})$ with $∣ u (x) ∣ \to 1$ as $∣ x ∣ \to \infty$ has fi…

math.AP2025

Sharp quantitative stability estimates for the Brezis-Nirenberg problem

Haixia Chen, Seunghyeok Kim, Juncheng Wei

We study the quantitative stability for the classical Brezis-Nirenberg problem associated with the critical Sobolev embedding $H_{0}^{1} (Ω) ↪ L^{\frac{2 n}{n - 2}} (Ω)$ in a…

math.AP2025

Compactness and non-compactness theorems of the fourth- and sixth-order constant $Q$ -curvature problems

Liuwei Gong, Seunghyeok Kim, Juncheng Wei

We provide a complete resolution to the question of compactness for the full solution sets of the fourth-order and sixth-order constant $Q$ -curvature problems on smooth closed Riem…

math.AP2024

Sharp quantitative stability estimates for critical points of fractional Sobolev inequalities

Haixia Chen, Seunghyeok Kim, Juncheng Wei

By developing a unified approach based on integral representations, we establish sharp quantitative stability estimates for critical points of the fractional Sobolev inequalities i…

Sharp stability for mixed bubbles on hyperbolic space

On critical dimensions for compactness in the boundary Yamabe problem, I

On Brezis' open problem 2.2

Nonradial stable solutions near the Joseph--Lundgren threshold

On Sirakov's equal-frequency uniqueness conjecture

Finite Potential Energy for Entire Solutions of the Planar Ginzburg--Landau Equation

Sharp quantitative stability estimates for the Brezis-Nirenberg problem

Compactness and non-compactness theorems of the fourth- and sixth-order constant Q-curvature problems

Sharp quantitative stability estimates for critical points of fractional Sobolev inequalities

Compactness and non-compactness theorems of the fourth- and sixth-order constant $Q$ -curvature problems