Author

Guo-Lin Qin

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Preprint Aug 2026

Optimal Rigidity Results for the $k$-Hessian Equation of Lane--Emden Type

In this paper, we establish optimal Liouville theorems and classification results for the $k$-Hessian Lane--Emden equation \[ \sigma_k(-D^2u)=u^p\quad\text{in }\R^n,\qquad -D^2u\in\overline{\Gamma_k},\qquad u\geq 0, \] where $2\leq k<\frac{n}{2}$ and $p>0$. Let $p_- = \frac{nk}{n-2k}$ and the critical Hessian--Sobo...

Wei Dai, Jingze Fu, Chang-Feng Gui et al. · 0 citations

Preprint Aug 2026

Smooth Failure of Boundary Unique Continuation for Harmonic Functions

For every $n\geq 3$, we construct a nonconstant real-valued function $U\in C^\infty(\overline{\mathbb R^n_+})$, harmonic in the upper half-space, whose complete boundary jet vanishes on a compact nowhere dense subset of $\partial\mathbb R^n_+$ of positive $(n-1)$-dimensional measure. The essential construction takes pl...

Guo-Lin Qin, Wei-Cheng Zhan · 0 citations