7 problems

Błocki's conjecture. Every $m$-subharmonic function should be locally $L^p$ integrable for every

Let $\Omega\subset\mathbb{R}^d$ be an open subset with smooth boundary. For $\lambda\in C^\infty(\overline{\Omega})$ with $\lambda>0$ on $\overline{\Omega}$, and…

PTW's optimality conjecture. The constant $e$ in this embedding is optimal: it cannot be replaced by any smaller universal constant.

Let $\Omega\subset \operatorname{\mathbb{R}}^d$ be a domain, and let $u\geq 0$ be subharmonic in $\Omega$, with $u$ not identically zero in $\Omega$. For an admissible disc…

Let $\rho\colon\mathbb{R}^n\to[0,1]$ be a measurable function with compact support. For $0\leq\alpha<n$, define its Riesz potential by … where $d_\omega x=\frac{1}{\omega_n}\,dx$ a…

Let $D$ be a domain, let $z_0\in D$, and let $\mu_n\in J_{z_0}(D)$ be a sequence of Jensen measures that is increasing in the order $\prec$ on $\operatorname{sbh}(D)$: … Assume tha…

Separate subharmonicity conjecture. If $F$ is subharmonic with respect to every pair $(x_j,x_{j+d})$, then $F$ is non-negative. This geometric statement is intended to provide the…