Jingze Fu

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...